Chapter 4. Examination of Tsunami Propagation Calculations
4.1. Governing equations and numerical scheme
4.1.1. Governing equations and numerical scheme for near-field tsunami propagation
The governing equations and numerical schemes based on the method proposed by Goto (Gotoand Ogawa, 1982) are shown below.
(1) Governing equations
1) Continuity equation

 M
N
0


y
x
t
2) Momentum equations 2M 2M 
M
M2  N2
  M 2    MN 

2 M

 


 K h 0  gDb2tx  D  y  D 
xD2
y 2 
 x
 2N 2N 
N
M2 N2
  MN    N 2 

2 N

  gD K h 



0


b
2
t
x  D  y  D 
yD2
 y 2  xwhere x and y are horizontal axes, t is time, η is the vertical displacement of water surface
above the still water surface, M and N are the flow rate per unit width in the x and y directions, his the still water depth, D is total water depth (D = h + η), g is the gravitational acceleration, Kh
is horizontal eddy viscosity coefficient, γb2 is friction coefficient (= gn2 / D1/3), n is Manning’s
coefficient of roughness.
(2) Numerical scheme
An overview of numerical scheme is given below.
• The time integration scheme is principally based upon the Leap-frog method.
• The arrangement of variables is based on the staggered grid (Figures 4.1.1-1 and 4.1.12).
• The primary upwind difference method is used for conservative advection terms.
• Friction terms are implicitly approximated for stable of calculation.

Appendix 4- 1

yN ik, j 11/ 2/ 2

j+1

η
●

Still water
surface
静水面

j

x

y

ik, j 1

M ik11/ /22, j

M ik11/ /22, jNhN ik, j 11/ 2/ 2

j-1

M

i-1

Figure 4.1.1-1 The arrangement of variables

x

i

i+1

Figure 4.1.1-2 The point schematics for the
staggered grid(3) Truncation error
For simplicity, when the governing equations are:

 M

0
t
x
M   M 2   gD 0t x  D 
xThen truncation error is given using the following equations.

 3 M 1 
3M  (t ) 2 3  (x) 2
0
t x 24 t
x 3 
A

 3 
 1 
3M
M   M 2 M 2M  gD  (t ) 2 3  gD(x) 2 3   x0
 x 24 t x  D 
D x 2
t
x 
B

C

A and B, which are underlined in the above equation, are numerical variance terms, and C
is the numerical viscosity term. Numerical viscosity term C is derived from the advection term
and functions so that wave height does not attenuate, and its effect also increases the greater △ 𝑥
becomes. The numerical variance terms have a greater effect when there is significant forwardtilting of the wave.
4.1.2. Governing equations and numerical schemes for far-field propagation of tsunamis(1) Governing equations
The linear Boussinesq theory (Boussinesq, 1872), which takes into account Coriolis force,is used.
1) Continuity equation

Appendix 4- 2

1   M cos   N 

＋
＋ ＝０
t R cos   2) Momentum equations
M gh 1  h3   fN 
 F
t
R 
R   3 
N
gh 
1
  h3  fM 
 Ft
R cos  
R cos    3 

However,F  2 2v 
1



cos

u


t  R cos   tuM  h, v  N   h 

where, λ and  are latitude and longitude, η is the vertical displacement of water
surface above the still water surface, M and N are the flow rate per unit width in the λ and directions, h is still water depth, g is the gravitational acceleration, f is Coriolis
coefficient, and R is Earth’s radius.

(2) Numerical scheme
In accordance with Goto and Sato (1993) and Goto et al. (1988) are shown below.
• Arrangement of variables: Staggered mesh
• Time integration scheme: Implicit method
4.1.3. Dispersive wave theory(1) Linear dispersive wave theory
In cases where the conditions for hydraulic quantities are:• Wave height-water depth ratio ε=η/h≪1• Relative water depth σ=h/L≪1• Ursell number Ur=ε/σ2≪1Then, the linear Boussinesq equations are used as shown below.
 M N


0
t
x
y
 h  h 2
M  h3
 Q1   Q1  ghtx x  3
 x  2 h  h 2
N  h3
 Q1   Q1  ghty y  3
 y  2Appendix 4- 3

where,Q1  2u  2v
tx ty(2) Nonlinear dispersive wave theory
In cases where the conditions for hydraulic quantities are:• Wave height-water depth ratio ε=η/h≪1• Relative water depth σ=h/L≪1• Ursell number Ur=ε/σ2~1
Then, the equations of Peregrine (1967) are used as shown below.
 M N
0


t
x
y

 h  h 2
   h 3
M   M 2    MN 
h2  
 Q1  
Q 2   
Q1  hQ 2   g h   x x  3
t x  D  y  D 2 x  2 h  h 2
   h 3
N   MN    N 2 h2  g h    Q1  
Q 2    Q1  hQ 2 
  
t x  D  y  D y y  32
 y  2


where,Q1 

 2u  2 v
tx ty

Q2   h    h 
u   v t  x  t  y 

Moreover, in cases where• Wave height-water depth ratio is ε=η/h ~1• Relative water depth is σ=h/L≪1• Ursell number is Ur=ε/σ2≫1Then, the equations of Goto (1984) are used as shown below.
 M N
0


x y
t

M   M 2    MN    
  g h   x
t x  D  y  D 
3h   2 H   h  h   2 H  h   H   h   

H
1
2
1
2

x  32
 x  2
2
N   MN    N   g h   
 
 
y
t x  D  y  D 3h   2 H   h  h   2 H  h   H   h   

H
1
2
1
2

y  32 y  2


where,

Appendix 4- 4  u v   u v 

 
 
H 1    u
 v 
xy  x y   x y 
 t

2


h 

  h v 
 v  u
H 2    uy xy  x
 t

4.1.4. Examination of dispersibility
4.1.4.1. Examination of tsunami numerical models accounting for dispersibility and wave breaking
When a tsunami propagates across a gently shelving coastline, the wave crest may fragment. Thisis known as soliton fission, which results from the effects of the wave’s nonlinearity and dispersibility.
When soliton fission occurs, the height of the tsunami wave is further amplified and it turns into awave breaking later on. Matsuyama et al. (2005) conducted shallow water deformation hydraulicmodel experiments of tsunami along gently shelving coastlines to ascertain the characteristics ofsoliton fission phenomena and wave breaking Using these results, Matsuyama et al. (2006) reviewed
the applicability of variance terms and made improvements in the wave breaking model.
(1) Experiments on soliton fission and wave breaking (Matsuyama et al., 2005)
Matsuyama et al. (2005) reproduced tsunami soliton fission using non-distortion
experiments simulating a continental shelf to ascertain phenomena near wave breaking andexamine wave breaking conditions, and then, using water level time-series data from experimentresults, proposed a method for calculating the ratio of water surface current velocity to wave
velocity, which is shown below, and the water surface slope as indicators of the wave breaking
threshold.
2
uS 
h   2   
D
2
 


 t  c
D 3 Dc 2  t 2 

where, t is time, η is the vertical displacement of water surface above the still water surface, us iswater surface horizontal current velocity, h is still water depth, D (=h+η) is total water depth,
and c is wave velocity.
The results of applications of experiment data show that the maximum water surface slope
for the wave breaking threshold is between 20 and 50° and the ratio of the water surface flow
current velocity to wave velocity is generally between 0.5 and 1.2, clearly indicating larger wave
breaking threshold values than those previously used.
(2) Variance term
When numerical calculations were conducted of variance term DT in a nonlinear dispersive
Appendix 4- 5wave equation using a one-dimensional cross-section and comparisons made of spatial tsunami
shape error and wave form just prior to breaking, it became clear that the use of variance terms
proposed by Peregrine (1967) as well as Madsen and Sørensen (1992), which are given below,
provides results approaching those obtained during experiments.
Peregrine (1967)

1 3 M: DT  h 2
3 t x 2

  3 2 3 M1
 gh3  3 
Madsen and Sørensen (1992) : DT  h 2
2
5 t x 15
 x 

(3) Wave breaking model (Matsuyama et al., 2006)
To express the attenuation of breaking soliton fission waves, Iwase et al. (2001) and Sato
(1995) incorporated a diffusion-type wave breaking attenuation term in the equation of motion.
Iwase et al. (2001) indicated that amplification could not be reproduced of highly nonlinear waves
where models for weak nonlinear dispersive waves exceed a ratio of 0.6 for the maximum waterlevel to water depth. Then, Iwase et al. (2001) provided a negative diffusion coefficient just prior
to the wave breaking to reproduce wave height amplification immediately prior to the wave
breaking This model specifies the wave height amplification region just prior to the wave
breaking and the attenuation region just prior to the wave breaking. However, it uses the ratio of
maximum water level to water depth as an indicator for detecting the region giving the artificial
amplification term, so there is a problem in that detection is delayed in the calculation with respect
to leading waves preceded by drawback and the wave breaking are also delayed. So, Matsuyama
et al. (2006) improved the detection indicator and diffusion coefficient. Figure 4.1.4-1 provides
an overview of this. The points improved are described below.
As for the parameters for initiation of the artificial amplification term, the following
parameters are used. Also, Split wave height H is used in place of the previously used water level
for the representative length in the diffusion coefficient when the wave is breaking.

D  2
3 x 2    gD H
where,  is diffusion coefficient and μ is coefficient, and the values are determined byexperiment data. ωs is the non-dimensional curvature of the water surface across the entire water
depth, and increases as soliton fission develops short-period waves. For wave height H, a large
value is adopted from among the heights from the wave crests to wave troughs when a trough is
cut out from troughs in split waves. These improvements have increased the reproducibility ofsoliton fission phenomena at the head of the leading wave after the backrush.
Reproducibility was the best when calculations were performed using the following values
Appendix 4- 6

which are based on parametric studies conducted of wave breaking locations and wave breaking
heights (water levels) as well as upon experiment data from three parametric studies: ωs when
the artificial amplification term is initiated, coefficient μ for the artificial amplification term, andthe wave breaking threshold γ (=us/c).
Start of artificial
amplification

Wave breaking point
End of breaking point

Start of cuttingout the wave
Wave crest line

Amplificationarea

Damping area

Artificial
amplification

Wave breaking(ωs, μ, γ)= (0.03, 0.09, 0.85)

Figure 4.1.4-1 Improved model of wave breaking (JSCE, 2007)
4.1.4.2. Examination of the occurrence of dispersive waves(1) Examination of dispersibility in deep sea areas
According to Iwase et al. (2002), when high-frequency content is included in the initialtsunami source, there are cases where wave number dispersibility may not be disregarded evenfor a tsunami that occurs in areas closer than 100km from shore. The effect of wave number
dispersibility in deep-sea areas is attenuation of the water level of the first tsunami wave, and isexpressed in the extension of wavelength and generation of a variance wave series. Iwase et al.
(2002) proposed an indicator value ID that quantitatively expresses the effect of this wave number
dispersive effect.

ID   h /W

(α = 101.76+0.001δ, β = 1.28 - 0.005δ)

where, h is the mean water depth at the tsunami source region, W is the fault width, and δ isthe fault dip angle. Iwase et al. (2002) focused on the elongation rate of the length of the firstwave, and stated that wave number dispersibility in deep-sea areas may be disregarded in cases
where the indicated value is smaller than 1.
The water level is focused here and a parametric study was conducted by a one-dimensional
propagation calculation using a nonlinear dispersive wave model and a nonlinear longwave
model. The relationship among fault upper edge depth, sea bottom topography slope, slip amountand strike with respect to the indicator values is investigated and the applicability of the indicatorvalues is examined.
Appendix 4- 7

1) Parameters accounting for variation
For the following parameters, their variations are taken into account. Those marked witha ● are items not included in the ID indicator value equation proposed by Iwase et al. (2002).
■

Tsunami source location depth:

1,000m, 2,000m■

Fault width:

15km, 50km, 100km■

Dip angle:

90°, 60°, 30° and 15°● Sea bottom topography slope:

1/100, 1/200● Strike:

0° (land-side hanging wall),180° (land-side foot wall)● Upper edge depth:

1.0km, 2.5km, 4.0km● Slip amount:

4.0m, 7.0m

2) Computational region
Two patterns of sea bottom topography with slopes 1/100 and 1/200 are applied, and theland-side region extends up to location of a water depth of 150m (Figure 4.1.4-2).
3) Initial water level
The initial water level is set as the level of the central cross-section of the grounddeformation distribution obtained by the method proposed by Mansinha and Smylie (1971).
4) Calculation results
Calculations are performed using the nonlinear dispersive wave model and nonlinear
long-wave model, and a comparison made of chronological tsunami shapes at points where thewater depth is 200m to find the correlation between the maximum water level ascent ratio(nonlinear long-wave / nonlinear dispersive wave) and the ID.
First, the impact is verified that parameters, which are not included in the ID, have on thewater level at points where the water depth is 200m. With respect to the direction of fault dip
angle, in cases where the land is a hanging wall, the results for the nonlinear wavelength model
for all cases exceed the results for the nonlinear dispersive wave model (Figure 4.1.4-3a). With
respect to slip amount, the distribution of the water level ratio is almost the same for cases of
4m and 7m (Figure 4.1.4-3b). With respect to the differences in sea bottom topography slope,no correlation with the ID is observed (Figure 4.1.4-3c). With respect to the upper edge depth,
a trend was observed: the deeper the edge became, the closer the ratio to 1, but no correlation
with the ID indicator value is observed (Figure 4.1.4-3d).
Figure 4.1.4-4 shows four patterns divided, according to size compared to the ID of 1 anda 10% error in the water level ratio.The issue here is that, in the cases where the ID is less than
1 and the water level ratio is greater than or equals to 10% respectively, the calculated waterlevel is greater for the nonlinear long-wave model in most cases. Although the calculated water
Appendix 4- 8

levels are lower for the nonlinear long-wave model in several cases, the setting of these cases
are not realistic because of a fault width of 100km and a dip angle of 60° (Table 4.1.4-1).
On the other hand, in several cases where the ID and the water level ratio are greater thanor equals to 1 and 10% respectively, there are cases that the calculated water level is smaller
for the nonlinear long-wave model and the source setting is realistic.
Therefore, it is believed to be no issues present for the use of the ID as an indicator for
determining whether or not to take into account the effect of wave number distribution in deepsea areas from the standpoint of the offshore water level.

Figure 4.1.4-2 Computational Region

Appendix 4- 9

a Effect of the fault dip angle directionb Effect of the slip amountc Effect of the topography slope
d Effect of the upper edge depth*long/disp (Nonlinear long-wave model / Nonlinear dispersive wave model)

Figure 4.1.4-3 The relationship between the maximum depth ratio where the depth is 200m (Nonlinear
long-wave model / Nonlinear dispersive wave model) and the ID indicator value (1))

Appendix 4- 10

Figure 4.1.4-4 The relationship between the maximum water level ratio where the depth is 200m
(Nonlinear long-wave model / Nonlinear dispersive wave model) and the ID indicatorvalue (2))

Table 4.1.4-1 The cases of which ID is less than 1 and the maximum water level ratio is less than orequals to 0.9
Sourcelocation
depth(m)1,000*long/disp（Nonlinear long-wave model/Nonlinear dispersive wave model）
Fault
Upper
Sea bottom
Slip
Width
dip Direction of edge
ID
topographyamount(km)
angle
fault dip
depth
slope
(m)
(km)
（°）
2.5
4
4
1/100
2.5
7
4
Land-side
100
60
0.72
foot wall
2.5
4
4
1/200
2.5
7
4

long/
disp
0.79
0.84
0.79
0.84
0.81
0.82
0.84
0.81

(2) Examination of grid partitioning for deep sea areas
Calculations are performed using a nonlinear dispersive wave model with a one-dimensionalcross-section and varied grid sizes for a case in which variance waves occurred offshore, and thencomparisons are conducted of spatial and chronological tsunami shapes at points having a water
depth of 400m to examine grid partitioning in deep-sea areas.
1) Computational region
Figure 4.1.4-5 shows topography of the computational region for the examination of grid
sizes in deep sea areas.

Appendix 4- 11

Figure 4.1.4-5 The computational region for the examination of grid sizes in deep sea areas
2) Tsunami source specifications, etc.
• Width 15km, dip angle 90°, slip angle 90°, slip amount 7m, upper edge depth 2.5km,
initial movement of leading wave
• Sea bottom topography slope: 1/100• Tsunami source location depth: 1,000m and 2,000m
3) Initial water level
The initial water level is set as the level of the central cross-section of the grounddeformation distribution obtained by the method proposed by Mansinha and Smylie (1971).
4) Calculation cases (grid sizes)
Other than CASE 0, calculations are performed up to a water depth of 150m at fixed grid
sizes for the entire region in all cases, and transmission conditions are set for the coastal boundary.
CASE 0 is calculated up to the coastline.
CASE 0: 30m grids for water depths deeper than 80m
and 10m grids for water depths shallower than 80m
CASE 1: 1,600m grid
CASE 2: 800m grid
CASE 3: 400m grid
CASE 4: 200m grid
CASE 5: 1,920m grid
CASE 6: 960m grid
CASE 7: 480m grid
CASE 8: 240m grid5) Calculation results
Comparisons are conducted focusing on the first wave of the main tsunami using 30m
grids as the base case for spatial and chronological tsunami shape (Figures 4.1.4-6 and 4.1.47). The difference is small between tsunami shapes of 800m grids and 30m grids.
Appendix 4- 12

Next, wave height and inherent period for the main tsunami and variance waves aredefined as shown in Figure 4.1.4-8 to find the water level and inherent period (peak to peak)from the first to the fifth waves (Table 4.1.4-2) and the ratios in comparison to CASE 0 are
arranged in Table 4.1.4-3. The results show that the 800m grid (CASE 2) is within 5% for boththe case of a tsunami source location depth of 1,000m at 0.96 and the case of a tsunami source
location depth of 2,000m at 0.97. It is found that, in partitioning grids for deep sea areas, a
1,600m grid is too rough, but the precision may be assured if the grid is set at 800m.

a) Spatial tsunami shapes after 1,000 second (Tsunami source location depth 1,000m)b) Spatial tsunami shapes after 2,000 seconds (Tsunami source location depth 2,000m)
Figure 4.1.4-6 Comparison of spatial tsunami shapes

Appendix 4- 13

Figure 4.1.4-7 Chlonogical tsunami shapes at where the depth is 400m
Appendix 4- 14

P0: Rise peak of the main tsunami
P1: The first inflection point since the water level went below zero after P0.
P2~P7: Peaks of dispersive waves after P1
T0: The elapsed time from the timing when water level first displaced by 10cm
from the initial level, and P1
T1: The elapsed time between P1 and P3
T2: The elapsed time between P3 and P5
T3: The elapsed time between P5 and P7
T = (T1+T2+T3) /3 … Mean period of three dispersive waves
H0: Wave height of the main tsunami (P0-P1)
H1~H6: Wave heights of dispersive waves (|P(n+1)-P(n)|)
H = (H1+H2+H3+H4+H5+H6) /6 … Mean height of three dispersive waves
Figure 4.1.4-8 The definition of wave height and inferential period of the main tsunami and dispersive
waves

Appendix 4- 15

Table 4.1.4-2 The water level and inherent period (peak to peak) from the first to the fifth waves* Unit: Water level(m), Period(minutes)
Source location depth: 1,000m
P1
CASE0
CASE1
CASE2
CASE3
CASE4
CASE5
CASE6
CASE7
CASE8

1.19
1.06
1.15
1.18
1.19
1.02
1.13
1.17
1.18

P2

P3

-0.20
0.20
-0.04
-0.15
-0.19
0.32
0.01
-0.14
-0.18

-0.03
0.24
0.08
0.00
-0.02
0.32
0.11
0.01
-0.02

P2

P3

P4
0.02
0.22
0.09
0.04
0.02
0.28
0.12
0.05
0.03

P5
0.03
0.20
0.09
0.05
0.04
0.25
0.11
0.05
0.04

T1
2.96
3.76
3.21
3.03
2.98
4.03
3.30
3.05
2.97

T2
1.39
1.97
1.56
1.43
1.40
2.19
1.62
1.45
1.40

T3
1.20
1.74
1.36
1.24
1.21
1.95
1.42
1.26
1.22

T4
1.10
1.62
1.25
1.14
1.12
1.83
1.31
1.16
1.12

Source location depth: 2,000m
P1
CASE0
CASE1
CASE2
CASE3
CASE4
CASE5
CASE6
CASE7
CASE8

0.96
0.84
0.93
0.95
0.96
0.81
0.91
0.94
0.95

0.69
0.80
0.74
0.71
0.70
0.82
0.74
0.71
0.70

0.51
0.60
0.54
0.52
0.51
0.62
0.55
0.52
0.51

P4
0.40
0.49
0.43
0.41
0.40
0.51
0.44
0.41
0.40

P5
0.33
0.42
0.36
0.34
0.33
0.45
0.37
0.34
0.33

T1
3.80
4.37
3.96
3.84
3.81
4.58
4.02
3.85
3.81

T2
2.12
2.52
2.22
2.14
2.12
2.68
2.27
2.15
2.12

T3
1.80
2.16
1.89
1.83
1.81
2.30
1.93
1.84
1.81

T4
1.64
1.96
1.72
1.66
1.64
2.10
1.75
1.67
1.64

Table 4.1.4-3 The ratios in comparison to CASE 0 of the water level and inherent period (peak to peak)
Source location depth: 1,000m
P1
CASE0
CASE1
CASE2
CASE3
CASE4
CASE5
CASE6
CASE7
CASE8

1.00
0.89
0.96
0.99
1.00
0.86
0.95
0.98
0.99

P2

P3

P4

1.00
-1.02
0.22
0.77
0.93
-1.61
-0.03
0.68
0.90

1.00
-7.89
-2.46
-0.01
0.69
-10.29
-3.58
-0.40
0.57

1.00
11.93
5.06
2.17
1.35
15.05
6.43
2.61
1.48

P2

P3

P4

P5
1.00
6.04
2.76
1.49
1.14
7.60
3.38
1.68
1.20

T1
1.00
1.27
1.08
1.02
1.01
1.36
1.11
1.03
1.00

T2
1.00
1.42
1.12
1.03
1.01
1.58
1.17
1.04
1.01

T3
1.00
1.45
1.13
1.03
1.01
1.62
1.18
1.05
1.01

T4
1.00
1.47
1.13
1.03
1.01
1.66
1.18
1.05
1.01

Source location depth: 2,000m
P1
CASE0
CASE1
CASE2
CASE3
CASE4
CASE5
CASE6
CASE7
CASE8

1.00
0.88
0.97
0.99
1.00
0.84
0.95
0.98
0.99

1.00
1.15
1.06
1.02
1.00
1.18
1.07
1.02
1.00

1.00
1.18
1.06
1.02
1.00
1.22
1.07
1.02
1.00

1.00
1.22
1.07
1.02
1.00
1.28
1.09
1.02
1.00

P5
1.00
1.26
1.08
1.02
1.00
1.34
1.10
1.02
1.00

Appendix 4- 16

T1
1.00
1.15
1.04
1.01
1.00
1.21
1.06
1.01
1.00

T2
1.00
1.19
1.05
1.01
1.00
1.27
1.07
1.02
1.00

T3
1.00
1.20
1.05
1.01
1.00
1.28
1.07
1.02
1.00

T4
1.00
1.20
1.05
1.01
1.00
1.28
1.07
1.02
1.00

(3) Examination of grid partitioning for shallow sea areas
For shallow regions (water depths between 50m and 400m), an examination of the grid
partitioning is conducted for performing calculations using a nonlinear dispersive wave model.
For the examination, numerical tests are conducted using one-dimensional tsunami propagation
calculations similar to the examination conducted of deep sea areas. For tsunami having a 180second period, grid sizes are set so that they were 1/20 or less of the wavelength for each section
representing water depth, and comparisons are conducted between cases where these grid sizes
were the base case (1/20 of the wavelength) and a case where the grid size was halved.
The initial water level for calculation is the level of the central cross-section of the grounddeformation distribution obtained by the method proposed by Mansinha and Smylie (1971). The
sea bottom topography slope is the same as that used in the examination of deep-sea areas, andthe tsunami source set position is 1,000m. Also, transmission conditions are configured for bothoffshore and on land.
For the default parameters, the five tsunami sources shown in Table 4.1.4-4 are used, andcomparisons conducted of the chronological tsunami shapes at a depth of 50m as well as the
maximum water level ascent and descent. Also, the base case for regions having a water depth ofgreater than 80m used a grid size of 30m and for regions where the water depth was 80m or
shallower, the grid size for the base case is 10m, and the ratio in relation to the base case isinvestigated (Tables 4.1.4-5 to 4.1.4-7).
The ratios of the maximum water level ascent and descent are within 5% in relation to thebase case, for both base case and the halved base case. It was confirmed, from the verification ofchronological tsunami shapes in Figure 4.1.4-9, that no significant difference is found on
fluctuation of the water level of the first wave, even when the grid size is set as 800m for regions
deeper than 400m, and set as base case for regions of 50m to 400m depth.
Although a delay in arrival time is observed, this is because the grid size offshore is set as
800m, and not because of setting the grid size for regions shallower than 400m.

Appendix 4- 17

Table 4.1.4-4 The fault parameters for the examination of grid sizes in shallow sea area
SourceWidth(km)

Fault dip
angle (°)

Upper edge
depth
(km)

Slip amount(m)

Slip angle
(°)

F1

100

15

2.5

7

90

F2
F3
F4
F5

17.3
50
15
50

60

2.5

20

9.44

2.5

90

9.7

2.5

45

4.16

0

5

90
90
90
270

Direction of
fault dip
Land-side footwall
Land-side hangwall
Land-side footwall
Land-side hangwall
Land-side hangwall

Table 4.1.4-5 The grid sizes for the tsunami of a 180-second period
Depth
(m)

Wave length
(m)

Wave
length/20(m)base case grid
size
(m)

20
30
40
50
60
70
80
90
100
150
200
250
300
350
400

2,520
3,086
3,564
3,984
4,365
4,714
5,040
5,346
5,635
6,901
7,969
8,910
9,760
10,542
11,270

126
154
178
199
218
236
252
267
282
345
398
445
488
527
563

100
100
100
200
200
200
200
200
200
200
400
400
400
400
400

Halvedbase casegrid size
(m)
50
50
50
100
100
100
100
100
100
100
200
200
200
400
400

Table 4.1.4-6 The maximum water level ascent at a depth of 50m

F1
F2
F3
F4
F5

grid size
30m and 10m(A)base casegrid size
(B)

3.26
3.96
4.88
1.16
1.28

3.23
3.84
4.87
1.10
1.34

Halvedbase casegrid size
(C)
3.24
3.86
4.86
1.12
1.30

Appendix 4- 18(B) / (A)(C) / (A)

0.99
0.97
1.00
0.95
1.05

0.99
0.98
1.00
0.96
1.02

Table 4.1.4-7 The maximum water level descent at a depth of 50m

F1
F2
F3
F4
F5

grid size
30m and 10m(A)

Base casegrid size
(B)

-1.77
-2.64
-1.58
-1.87
-2.99

-1.77
-2.71
-1.62
-1.85
-2.94

Halvedbase casegrid size
(C)
-1.78
-2.74
-1.59
-1.87
-2.96

Appendix 4- 19(B) / (A)(C) / (A)

1.00
1.02
1.03
0.99
0.98

1.01
1.04
1.01
1.00
0.99

Figure4.1.4-9 Chronogical tsunami shapes at a depth of 50m

Appendix 4- 20

4.1.5. Examination of field applicability of the nonlinear dispersive wave model(1) Calculation conditions
A nonlinear dispersive wave model having a two-dimensional plane was used for a tsunami
analysis to examine applicability in the field. The tsunami, which was the object of theexamination, was the 1933 Showa Sanriku tsunami, and the fault model is shown in Table 4.1.51. The principal calculation conditions are consolidated in Table 4.1.5-2. Also, Kuji Bay was thesite for the case study in this examination. The grid partitioning of the Sanriku coastline is shownin Figures 4.1.5-1 and 4.1.5-2.
Table 4.1.5-1 Parameters of the fault model for the 1933 Showa Sanriku tsunami (JSCE, 2002)
Referencepoint

40.16°N
144.5°E

MW

Length
L
(km)

Width
W
(km)

8.4

185

50

Depth of upper
Strikeedge of thedirection
fault planeθ(degree)d(km)1

Dip angle
δ(degree)Slip angle
λ(degree)Slipamount
D(m)

45

270

6.6

180

Table 4.1.5-2 Calculation conditions
Non-linear dispersive

Non-linear long-wave

wave theory

theory800 ~ 12.5 m

800 ~ 12.5 m

0.1 s

0.1 s

Simulating time

2 hours

2 hours

Manning’s coefficient

0.03

0.03

central difference

1st-order upwind

schemedifference scheme

Matsuyama et al.(2006)-

Matsuyama et al.(2006)-

Peregrine(1967)-

Grid sizes
Computation time

Noteintervalof roughness
Advection term

Artificial amplification
term
Wave breaking term
Variance term

Appendix 4- 21

ωE =0.01, α=0.09
ωs =0.03,
β=0.23, γ=0.85

(m)

解析領域
Computational
regionGrid size

2000

800 m

4000

400 m

6000

200 m

a) Computational region

Grid size
100 m
400
300
0

50

100

200

b) Enlarged view
Figure 4.1.5-1 Grid division and water depth

Appendix 4- 22

50 m
25 m
12.5 m

(m)

20
0

40

60

80

Figure 4.1.5-2 Water depth of 12.5m grid region(2) Calculation results
In Figure 4.1.5-3, the propagation conditions of a tsunami from the tsunami source to thecoastline are shown with a spatial distribution of the water level, and a comparison is shown
between the dispersive wave model and the nonlinear long-wave model. According to these
diagrams, short-period waves repeatedly occur in tsunami source regions coastal regions one after
another with the nonlinear dispersive wave model. As the result, it may be said that it is desirable
to use the nonlinear dispersive wave model when precise of tsunami wave shapes occurring at
tsunami sources is an issue.
A cross-sectional view of the water level distribution of the target section of Kuji Bay given
in Figure 4.1.5-4 is shown in Figure 4.1.5-5. In the dispersive wave model, soliton fission begins
to occur as the tsunami arrives at the bay entrance until the vicinity of the central area (water
depth shallower than 20m), and becomes more pronounced as it nears the coastline. As a result,
the water rises due to the wave splitting near the shoreline. Also, soliton fission clearly occurs infront of breakwaters and other such areas, and an examination that takes into account soliton
fission is necessary in areas where split waves are predominant. Figures 4.1.5-6 and 4.1.5-7 show
the maximum tsunami height and the cross-sectional views analyzed using the dispersive wave
model and nonlinear long-wave model. This shows that in contrast to the nonlinear long-wave
model, the dispersive wave model affords a tendency for tsunami height along the coastline to begreater locally due to the effects of soliton fission and other factors, but there is almost no changewith respect to areas inundated or tsunami height in tsunami run-up areas.

Appendix 4- 23

(a) Non-linear dispersive wave theory(b) Non-linear long-wave theory0 h 0 min after0 h 0 min0 h 5 min0 h 5 min0 h 10 min

0 h 10 min

0 h 30 min

0 h 30 min

Figure 4.1.5-3 Comparison of the spatial distribution of tsunami water level

Appendix 4- 24

(m)

(A)

(B)
60

20

80

40

0

Figure 4.1.5-4 Cross section to compare the results
43 minutes after
Water depthLine (A)Non-linear long wave theory

Non-linear dispersive wave
theoryWater depthLine (B)

Water level (m)Non-linear dispersive wave
theoryWater level (m)Non-linear long wave theory

Distance (km)Distance (km)45 minutes after
Non-linear long wave theory

Water depth

Non-linear dispersive wave
theoryWater depth

Water level (m)Non-linear dispersive wave
theoryWater level (m)Non-linear long wave theory

Distance (km)Distance (km)47 minutes after
Water depth

Non-linear long wave theory

Non-linear dispersive wave
theoryWater level (m)Non-linear dispersive wave
theoryWater level (m)Non-linear long wave theory

Distance (km)Distance (km)Figure 4.1.5-5 Cross section of tsunami water level

Appendix 4- 25

Water depth(a) Non-linear dispersive wave theory(b) Non-linear long-wave theory

(A)
(B)
(C)
(D)
(E)
(F)

2.5 km(m)

Figure 4.1.5-6 Maximum water level distribution
Line (B)Line (A)Non-linear dispersive wave
theoryWater depth

Non-linear long wave theory

Maximum
Water level (m)Maximum
Water level (m)Non-linear long wave theory

Distance (km)Line (C)

Water depthDistance (km)Line (D)Non-linear long wave theory

Water depth

Non-linear dispersive wave
theoryWater depth

Maximum
Water level (m)Non-linear dispersive wave
theoryMaximum
Water level (m)Non-linear long wave theory

Non-linear dispersive wave
theoryDistance (km)Distance (km)Line (E)
Water depth

Non-linear long wave theory

Non-linear dispersive wave
theoryMaximum
Water level (m)Non-linear dispersive wave
theoryMaximum
Water level (m)Non-linear long wave theory

Line (F)Distance (km)Distance (km)Figure 4.1.5-7 Cross section of maximum water level distribution

Appendix 4- 26

Water depth

4.1.6. Verification of the appropriateness of three-dimensional models using simulation analysis ofprevious hydraulic model experiment results
In cases focusing on tsunami coastal propagation and land run-up, numerical models with a planetwo-dimensional field (plane two-dimensional model) that apply nonlinear long-wave theory (shallow
water equation) are often used. On the other hand, in recent years the development of fluid analysis
technology has also made it possible to apply three-dimensional fluid dynamics models (threedimensional models) that directly calculate three-dimensional basic equations.
Here, case studies have been consolidated of previous analyses of leading three-dimensionalmodels, and numerical simulations of previous hydraulic model experiments have been conducted toverify the appropriateness of three-dimensional models.
(1) Case studies of previous analyses of representative three-dimensional models
Three-dimensional models are broadly classified into models that assume hydrostaticpressure approximation and models that do not. STOC-ML and C-HYDRO3D are threedimensional models that consider hydrostatic pressure approximation, and CADMAS-SURF/3D,
OpenFOAM, STOC-IC, DOLPHIN-3D and tsunami complex disaster prediction model, andothers are examples of three-dimensional models that do not consider hydrostatic pressure.
1) CADMAS-SURF/3D
CADMAS-SURF/3D is a non-hydrostatic pressure-type three-dimensional model, which
was researched and developed by the Coastal Development Institute of Technology (2010),
and has the capability not only to calculate the behavior and pressure of tsunami running up
onto land, but also analyses that are coupled with gases, ground and solids. Arikawa et al.
(2005) verified the appropriateness of results of analyses of fluid behavior and tsunami wave
pressure conducted using CADMAS-SURF/3D based on comparisons with the results ofhydraulic model experiments on run-up tsunami (Figure 4.1.6-1).
2) OpenFOAM
Open source Field Operation and Manipulation (OpenFOAM) is a fluid analysis model
released as free and open source software under GNU General Public License (GPL). Fam etal. (2012) and Kawasaki et al. (2013) applied the OpenFOAM interFoam solver to numericalsimulations of problems of water column collapse and hydraulic model experiments of run-up
tsunami, and conducted comparative validations with the results of experiments on fluid
behavior and tsunami wave pressure.
3) Storm Surge and Tsunami Simulator (STOC)
The Storm Surge and Tsunami Simulator in Oceans and Costal Areas (STOC) is a hybrid
model capable of connecting, as necessary, the quasi-three-dimensional hydrostatic pressure
Appendix 4- 27

multi-level model STOC-ML to the three-dimensional non-hydrostatic pressure flow model
STOC-IC. Tomita and Kakinuma (2005), Tomita and Honda (2008), and Takahashi and Tomita(2013) used STOC to verify the model’s appropriateness and precision based uponcomparisons with hydraulic model experiments using factors such as slope, tsunami
breakwaters, actual topography, etc.
4) DOLPHIN-3D
Dynamic numerical model Of muLti-Phase flow with Hydrodynamic INteractions-3
Dimension version (DOLPHIN-3D) is a three-dimensional model of the non-hydrostaticpressure type that is capable of calculating the dynamic behavior of debris, interaction between
structures and tsunami, and behavior of run-up tsunami and other elements. Kawasaki et al.
(2006) as well as Kawasaki and Hakamata (2007) applied DOLPHIN-3D to numericalsimulations of hydraulic model experiments on tidal bore accompanying water column
collapse as well as collision and drift of rectangular rigid bodies to conduct a comparison andvalidation of the model against the results of experiments on fluid behavior and wave pressure.
5) Tsunami complex disaster predication model
The tsunami complex disaster prediction model is a non-hydrostatic pressure-type threedimensional model capable of calculating fluid motion as well as vessel motion and mooring
cable tension. Yoneyama et al. (2008) and Yoneyama and Nagashima (2009) used the tsunami
complex disaster prediction model to verify the appropriateness of results of analyses of runup tsunami behavior as well as debris behavior based upon comparisons with the results ofhydraulic model experiments.
6) C-HYDRO3D
C-HYDRO3D is a hydrostatic pressure-type three-dimensional model that calculates
tsunami propagation from the tsunami source region to the coastline as well as overflow andrun-up flow in addition to calculations of the motion of debris and topography change causedby tsunami. Kihara and Matsuyama (2010) and Kihara et al. (2012) verified the reproducibilityof tsunami behavior and topography change for the area around bays in Sri Lanka that werecaused by the 2004 earthquake tsunami off the coast of Sumatra as well as hydraulic modelexperiments, and they also validated the vertical distribution of suspended sedimentconcentrations using a comparison with moving-bed open channel experiments.

Appendix 4- 28

(1) Time series of wave height(2) Wave pressure acting on the seawall

Figure 4.1.6-1 Comparison of analysis results by CADMAS-SURF/3D with experimental results(Arikawa et al., 2005)(2) Numerical simulations of hydraulic model experiments reproducing tsunami behavior
overflowing seawalls and other facilities
Numerical simulations were conducted which applied a plane two-dimensional model andthree-dimensional model to hydraulic model experiments simulating tsunami behavior whenoverflowing seawalls to verify the appropriateness of both models.
1) Experiment overview
Arimitsu et al. (2012) used a rectangular water channel (height: 0.5m, width: 0.5m, length:18m), and quickly opened the gate to a water storage section, thereby causing a tidal-liketsunami. The tsunami propagated through a uniform water depth (length: 3.2m), overflowing
subsequent seawalls (heights: 0.02m and 0.05m) and running up onto a flat land area (length:6.8m). During the experiments, seawall height, storage water position, shape of structure
models, and the position where the structures settings were varied.
2) Examination conditions[1] Plane two-dimensional model
In analyzing tsunami, a method (Goto and Ogawa, 1982) was used that employs astaggered leapfrog method to differentiate continuity equation and nonlinear long-wave
theory.
The computational region, ground height, initial water level and other calculation
Appendix 4- 29

conditions were the same as those adopted for the experiments (Table 4.1.6-1, Figure 4.1.62). Also, for seawalls, two methods were used, one that uses the Honma model (Honma
formula) to calculate the overflow rate along the overflow boundary, and the other that
calculates the flow rate per unit width using nonlinear long-wave theory for the topography.
From the experiment conditions used by Arimitsu et al. (2012), a storage water level of
0.15m was used and there were no structure models, and three calculation cases configured
setting the seawall heights at 0.00m (no seawall), 0.02m, and 0.05m.
[2] Three-dimensional model
For this examination, CADMAS-SURF/3D (Coastal Development Institute ofTechnology, 2010), a numerical wave motion water channel program, is used.
The numerical experiment water channel, which is used for the numerical simulations,is the same as that for the plane two-dimensional model (Figure 4.1.6-2). Also the simulating
conditions of the three-dimensional model are shown in Table 4.1.6-2. The calculation cases
are the same three cases as for the plane two-dimensional model.
3) Numerical simulation results
The following knowledge was gained from the results of a comparison made of theempirical results and analytical results of spatial tsunami shapes in the area around seawalls aswell as chronological tsunami shapes of water level and flow velocity at the geodetic points inthe experiment.
[1] Tsunami behavior in sea areas
From chronological tsunami shapes of water levels in sea areas as shown in Figure
4.1.6-3, the plane two-dimensional model was not able to reproduce the variance effect of
the tsunami head as observed in experiments and three-dimensional models, and the phaseof the water level peak was also early, but, with the exception of these points, it was
confirmed that experiments were able to be nicely reproduced. Also, it was found that thethree-dimensional model properly reproduces the empirical results for both spatial tsunami
shapes and chronological tsunami shapes of water levels.
[2] Tsunami behavior on land
Using chronological tsunami shapes of water level and flow velocity in land areas asshown in Figures 4.1.6-4 and 4.1.6-5, with the exception of the area around seawalls, theresults of calculations using the plane two-dimensional model and three-dimensional model
were consistent with respect to conditions after run-up, and created good reproductions ofinundation depth and flow velocity in the empirical results. However, from spatial tsunami
shapes during overflow of seawalls as shown in Figure 4.1.6-6, the plane two-dimensionalmodel is not able to reproduce water surface shapes very near seawalls, so the threedimensional model is regarded as effective in cases where the inundation depth and flow
Appendix 4- 30

velocity need to be more appropriately ascertained.
Table 4.1.6-1 Simulating condition of two-dimensional model in the reproduction calculation of
hydraulic model experiments of Arimitsu et al. (2012)
Item

Setting value

Governing equations

Nonlinear long-wave theory

Computational region

The same region as the hydraulic model experiment

Grid sizes

1cm interval

Computation time interval

0.0002s (Considering C.F.L. condition)

Initial conditions

The same condition as the hydraulic model experiment

Offshore

Water storage wall: Complete reflection condition
Water channel side wall: Full reflection condition
Land part: Free transmission condition

boundary
conditions
OnshoreBoundary
conditions boundary

Wave front condition

conditions
Overflowboundary
conditions

Honma model

Manning’s coefficient

n=0.010 m-1/3·sof roughness
Simulating time

20s

6.8m
L4

3.2m

L3

L2

L1

8m

S1

seawall S2water storage area
0.2m

1m

1m

1m

1m

1m

0.5m

1m

* Water channel width: 0.5m, S1, S2, L1～L4: Measurement points of water level and flow
velocity
Figure 4.1.6-2 The numerical experiment water channel for the reproduction calculation of hydraulicmodel experiments of Arimitsu et al. (2012)

Appendix 4- 31

Table 4.1.6-2 Simulating condition of three-dimensional model in the reproduction calculation of
hydraulic model experiments of Arimitsu et al. (2012)
Item

Setting value
The same condition as the hydraulic model

Initial conditions

experiment
The same region as the hydraulic model

Computational region

Grid sizes

Time control

experimentx

0.01 ~ 0.03m

y

0.01m

z

0.01 ~ 0.025m

Computation time interval t

Automatic

Simulating time

15s

Difference scheme

VP-DONOR

Boundary

Velocity and pressure

Logarithmic law

conditions

VOF function

FREE

Density

1,000kg/m3

Acceleration of gravity

9.8m/s2

Viscosity

None

Bubble rising speed

0.2m/sWater droplets falling speed

Free fall

Flow velocity of surface cell

Zero gradient

Physicalproperty values

OptionAppendix 4- 32

S1 Water level

0.15
0.10
0.05

S2 Water level

0.20

Experiment
3D model2D model (topography)
Water level(m)Water level(m)

0.20

0.00

Experiment
3D model2D model (topography)

0.15
0.10
0.05
0.00

0

2

4

6

8
Time(s)

10

12

14

0

2

4

6

8
Time(s)

10

12

14

(1) In the case seawall height at 0.00m (No seawall)
S1 Water level

0.20

0.15
Water level(m)0.15Water level(m)S2 Water level

0.20

0.10

Experiment
3D model2D model (Honma formula)
2D model (topography)

0.05
0.00
0

2

4

6

8
Time(s)

10

12

0.10

Experiment
3D model2D model (Honma formula)
2D model (topography)

0.05
0.00

14

0

2

4

6

8
Time(s)

10

12

14

(2) In the case seawall height at 0.05m
Figure 4.1.6-3 Time series of water level at S1 and S2

L1 water level

3.00

Experiment
3D model2D model (topography)

0.15
0.10
0.05
0.00

Experiment
3D model2D model (topography)

2.00
1.50
1.00
0.50
0.00

0.20

2

4

6

8
Time (s)L2 water level

10

12

3.00

Experiment
3D model2D model (topography)

0.15

0.05
0.00
2

4

6

8
Time (s)

10

12

2

4

6

8
Time (s)L2 velocity

14

10

12

14

Experiment
3D model2D model (topography)

2.50

0.10

0

0

14

Flow Velocity (m/s)

0Inundation depth (m)L1 velocity

2.50
Flow Velocity (m/s)

Inundation depth (m)

0.20

2.00
1.50
1.00
0.50
0.00
0

2

4

6

8
Time (s)10

Figure 4.1.6-4 Time series of water level and flow velocity at L1 and L2(In the case seawall height at 0.00m)

Appendix 4- 33

12

14

3.00

L1 water level

Experiment
3D model2D model (Honma formula)
2D model (topography)

0.15
0.10
0.05
0.00
2

4

6

8
Time (s)

10

12

2.00
1.50
1.00
0.50

14

0

3.00

L2 water level

Experiment
3D model2D model (Honma formula)
2D model (topography)

0.15

2

4

6

8
Time (s)L2 velocity

0.10
0.05
0.00

10

12

14

Experiment
3D model2D model (Honma formula)
2D model (topography)

2.50
Flow Velocity (m/s)

Inundation depth (m)

0.20

2.00
1.50
1.00
0.50
0.00

0.20

2

4

6

8
Time (s)

10

12

0

14
3.00

L3 water level

Experiment
3D model2D model (Honma formula)
2D model (topography)

0.15

2

4

6

8
Time (s)L3 velocity

0.10
0.05
0.00

10

12

14

Experiment
3D model2D model (Honma formula)
2D model (topography)

2.50
Flow Velocity (m/s)

0Inundation depth (m)Experiment
3D model2D model (Honma formula)
2D model (topography)

0.00
0

2.00
1.50
1.00
0.50
0.00

0.20

2

4

6

8
Time (s)

10

12

0

14
3.00

L4 water level

Experiment
3D model2D model (Honma formula)
2D model (topography)

0.15

2

4

6

8
Time (s)L4 velocity

0.10
0.05
0.00

10

12

14

Experiment
3D model2D model (Honma formula)
2D model (topography)

2.50
Flow Velocity (m/s)

0Inundation depth (m)L1 velocity

2.50
Flow Velocity (m/s)

Inundation depth (m)

0.20

2.00
1.50
1.00
0.50
0.00

0

2

4

6

8
Time (s)

10

12

14

0

2

4

6

8
Time (s)10

Figure 4.1.6-5 Time series of water level and flow velocity at L1 and L2(In the case seawall height at 0.05m )Appendix 4- 34

12

14

Figure 4.1.6-6 Spatial waveform of the tsunami overflowing the seawall

Appendix 4- 35

(3) Numerical simulations of hydraulic model experiments simulating tsunami behavior running up
to buildings and other structures in land areas
Numerical simulations were conducted which applied a plane two-dimensional model andthree-dimensional model to hydraulic model experiments simulating the behavior of tsunami
running up to buildings on land.
1) Experiment overview
Arimitsu et al. (2013) used one side of the plane water tank (length: 38m, width: 20m,
height: 1.2m) shown in Figure 4.1.6-7 that was partitioned by guided wave panels in the centerand a wave-making machine to create solitary ways simulating a tsunami. The tsunami
propagates across an even floor 4.2m in length and the slope of sea bottom of 1/10 and 1/50,
overflows over an upright embankment that is 0.11m high, and runs up onto a flat land terrain.
The arrangement of the structure models is into patterns: a case where a rectangular structure(length: 0.1m, width: 0.1m, height: 0.4m) is arranged in a single unit (single unit) and a casewhere two of the same structures are set up offshore (group of structures) as shown in Figure
4.1.6-7. In the experiments, the height of the solitary waves as well as the position of thestructure settings were varied, and measurements taken of the water level and horizontal flow
velocity in the sea area (H1 ~ H3), as well as the inundation depth (L0 ~ L3) and flow velocity(L3) in the land area.

Figure 4.1.6-7 Experimental equipment and arrangement of the structures

Appendix 4- 36

2) Examination conditions[1] Plane two-dimensional model
In analyzing tsunami, a method (Goto and Ogawa, 1982) was used that employs astaggered leapfrog method to differentiate continuity equation and nonlinear long-wave theory.
The computational region ranged from the H2 point on one side (width: 9m) of the plane watertank to the tip of the land terrain as shown in Figure 4.1.6-7. Also, the analysis focused on
experimental cases where the arrangement of the structures was as a “group of structures”.
The simulating conditions for the plane two-dimensional model are given in Table 4.1.63. The conditions for the ground height and the initial water level are both the same as for theexperiments, and the water level at observation point H2, which was obtained from theexperiment, was set as the incident tsunami shape, and was launched from the offshore
boundary. The grid sizes were set for a total of six patterns, which were 1cm, 2cm, 2.5cm,
3.33cm, 5cm and 10cm so that the number of grids between structures (10cm) was 10 grids, 5grids, 4 grids, 3 grids, 2 grids, and 1 grid.
Table 4.1.6-3 Simulating condition of two-dimensional model in the reproduction calculation of
hydraulic model experiments of Arimitsu et al. (2013)
Item

Setting value

Governing equations

Nonlinear long-wave theory

Grid sizes

1cm, 2cm, 2.5cm, 3.33cm, 5cm, 10cm

Computation time interval

0.0002 ~ 0.0010s (Considering C.F.L condition)

Offshoreboundary
Boundary
conditions

conditions

Sea area: Inputting time series of water level of solitary wave
which tsunami height is 3cm
Water channel side wall: Full reflection condition
Land area: Free transmission condition

Onshoreboundary

Wave front condition

conditions
Manning’s coefficientof roughness
Simulating time

n=0.010 m-1/3·s
15s[2] Three-dimensional model
CADMAS-SURF/3D (Coastal Development Institute of Technology, 2010), a numericalwave motion water channel program, was used for the three-dimensional model. The
computational region and calculation cases were the same as for the plane two-dimensional
Appendix 4- 37

model.
The simulating conditions for the three-dimensional model are shown in Table 4.1.6-4.
The incident tsunami shape of a solitary wave (same tsunami shape as the plane twodimensional model) was input from the wave-making boundary of the sea area. With respect
to the grid sizes in the height direction, the minimum grid sizes were varied using 0.25cm,
0.5cm, and 1cm so that the number of grids for the inundation depth at L0 point in theexperiment would be 20 grids, 10 grids and 5 grids. The grid sizes in the horizontal direction
were set so that the ratio of the grid sizes in a horizontal direction to the height direction would
be either 2:1 or 1:1.
Table 4.1.6-4 Simulating condition of three-dimensional model in the reproduction calculation of
hydraulic model experiments of Arimitsu et al. (2013)
Item

Setting value･0.5cm×0.5cm×0.25cm

Grid sizes△x×△y×△z･0.5cm×0.5cm×0.5cm･1cm×1cm×0.5cm･2cm×2cm×1cm

Time control

Computation time interval △t

Automatic

Simulating time

15s

Offshore boundary conditions

Inputting time series of water level ofsolitary wave which tsunami height is 3cm

Difference scheme

VP-DONOR

Boundary

Velocity and pressure

SLIP

conditions

Scalar quantity

FREE

Density

1,000kg/m3

Acceleration of gravity

9.8m/s2

Viscosity

None

Bubble rising speed

0.2m/sWater droplets falling speed

Free fall

Physical property
values

Option3) Reproduction calculation results
With regard to the reproducibility of inundation depth and flow velocity for tsunami
overflowing seawalls or other structures up to the flooding of the site, the following knowledge
was gained from the results of analyses conducted that focused on the appropriate number ofgrids between structures and other elements, and the tsunami circling around behind the
Appendix 4- 38

structures.
[1] Plane two-dimensional model
Based on Figure 4.1.6-8, it is difficult for the plane two-dimensional model toreproduce sudden rises of water masses in front of structures. However, with the exceptionof such localized phenomena, the plane two-dimensional model allows for calculations ofinundation depth and flow velocity with good precision overall. However, in cases where
the number of grids between structures is either one or two, the reproducibility of inundation
depth after passing between the structures is significantly reduced, so it is desirable to set
the number of grids between structures at a minimum of three.
[2] Three-dimensional model
Based on Figures 4.1.6-9 and 4.1.6-10, the three-dimensional model allows forcalculation with good precision overall of sudden rises in water mass in front of structures,and use of the three-dimensional model is effective in cases where it is necessary to ascertain
in more detail the behavior of tsunami around structures. However, there are cases where
calculation precision of hydraulic quantity is reduced when grid sizes in a vertical direction
are rough, so this point needs to be kept in mind when setting grid sizes in the verticaldirection.

Appendix 4- 39

Inundation depth (m)0.10Experiment
2D model (1cm)
2D model (2cm)
2D model (2.5cm)
2D model (3.33cm)
2D model (5cm)
2D model (10cm)

L3 Inundation depth

0.08
0.06
0.04
0.02
0.00
4

Inundation depth (m)

0.10

5

6

7

8

9
Time(sec)

10

11

13

14

Experiment
2D model (1cm)
2D model (2cm)
2D model (2.5cm)
2D model (3.33cm)
2D model (5cm)
2D model (10cm)

L2 Inundation depth

0.08

12

0.06
0.04
0.02
0.00
4

5

6

7

8

9
Time(sec)

10

11Inundation depth (m)

0.10

13

14

Experiment
2D model (1cm)
2D model (2cm)
2D model (2.5cm)
2D model (3.33cm)
2D model (5cm)
2D model (10cm)

L1 Inundation depth

0.08

12

0.06
0.04
0.02
0.00
4

5

6

7

8

9
Time(sec)

10

11Inundation depth (m)

0.10

13

14

Experiment
Visual measuring(Experimental video)
2D model (1cm)
2D model (2cm)
2D model (2.5cm)
2D model (3.33cm)
2D model (5cm)
2D model (10cm)

L0 Inundation depth

0.08

12

0.06
0.04
0.02
0.00
4

5

6

7

8

9
Time (sec)1011Flow velocity (m/s)

2.0

13

14

Experiment
2D model (1cm)
2D model (2cm)
2D model (2.5cm)
2D model (3.33cm)
2D model (5cm)
2D model (10cm)

L3 Flow velocity

1.5

12

1.0
0.5
0.0
‐0.5
4

5

6

7

8

9
Time (sec)

10

11

12

13

14

Figure 4.1.6-8 Time series of inundation depth and flow velocity by experimental results of Arimitsu
et al. (2013) and numerical simulation results of plane two-dimensional model

Appendix 4- 40

Inundation depth (m)0.10Experiment
3D model (0.5×0.5×0.25cm)
3D model (0.5×0.5×0.5cm)
3D model (1×1×0.5cm)
3D model (2×2×1cm)

L3 Inundation depth

0.08
0.06
0.04
0.02
0.00
4

Inundation depth (m)

0.10

5

6

7

8

9
Time (sec)

10

12

13

14

Experiment
3D model (0.5×0.5×0.25cm)
3D model (0.5×0.5×0.5cm)
3D model (1×1×0.5cm)
3D model (2×2×1cm)

L2 Inundation depth

0.08

11

0.06
0.04
0.02
0.00
4

5

6

7

8

9
Time (sec)10

Inundation depth (m)

0.10

12

13

14

Experiment
3D model (0.5×0.5×0.25cm)
3D model (0.5×0.5×0.5cm)
3D model (1×1×0.5cm)
3D model (2×2×1cm)

L1 Inundation depth

0.08

11

0.06
0.04
0.02
0.00
4

Inundation depth (m)

0.10

5

6

7

8

9
Time (sec)

10

11

12

13

14

Experiment
Visual measuring(Experimental video)
3D model (0.5×0.5×0.25cm)
3D model (0.5×0.5×0.5cm)
3D model (1×1×0.5cm)
3D model (2×2×1cm)

L0 Inundation depth

0.08
0.06
0.04
0.02
0.00
4

5

6

7

8

9
Time (sec)10

Flow velocity (m/s)

2.0

12

13

14

Experiment
3D model (0.5×0.5×0.25cm)
3D model (0.5×0.5×0.5cm)
3D model (1×1×0.5cm)
3D model (2×2×1cm)

L3 Flow velocity

1.5

11

1.0
0.5
0.0
‐0.5
4

5

6

7

8

9
Time (sec)

10

11

12

13

14

Figure 4.1.6-9 Time series of inundation depth and flow velocity by experimental results of Arimitsu
et al. (2013) and numerical simulation results of three-dimensional model

Appendix 4- 41

(a) Side-view(b) Front-view

Figure 4.1.6-10 Tsunami behavior around structures of three-dimensional model(△x×△y×△z = 1cm × 1cm × 0.5cm)

4.2. Calculation method for distribution of vertical displacement on sea bottom surface
4.2.1. Method proposed by Mansinha and Smylie (1971)
In the initial conditions for tsunami propagation calculation, it is necessary to configure the
distribution of vertical displacement on the sea bottom surface. With respect to this verticaldisplacement distribution, methods proposed by Mansinha and Smylie (1971) as well as by Okada(1985) have been used for calculating the distribution of displacement of the surrounding groundaccompanying earthquake fault motion, which assume that the ground where an earthquake occurs is
an isotropic and homogeneous elastic body. Here, the method proposed by Mansinha and Smylie(1971) is shown below.
Displacement ui of the surrounding area due to the amount of discrepancy Δui in arbitrary closed
surface Σ of elastic half-space has been given below from Skeketee (1958).
Appendix 4- 42 u j u k  u 
u i    u j  jk  i    i  i   k dS

 

 
 k  j  where,  jk is the Kronecker delta,  and(4.2.1)

 are Lame’s constants, vk is the normal direction

cosine of dS, and u i j is displacement in direction i of points ( x1 , x2 , x3 ) due to units of power
working in j direction at points (1 , 2 , 3 ) .
For the local rectangular coordinates, as shown in Figure 4.2-1, the fault plane is extended andthe line (strike) intersecting with the sea bottom surface is x1 , the point where the center of thelongitudinal direction of the fault plane intersects with x1 is the origin (O), and the x 2 axis proceeds
to the right from O, and the x3 axis downward. Also, the line passing through the center of the fault
plane at O is the ξ axis (the ξ axis is within plane x2－x3 ).

O

δ

h1
h2

W

L
L

ξ

Figure 4.2-1 Fault geometry and coordinate system
The fault specifications are defined so that 2L is the fault length, h1 the length from the origin
along the ξ axis to the upper edge of the fault as shown in Figure 4.2-2, h2 the length down to the lower
edge of the fault (h2-h1 is width W of the fault), and δ the fault dip angle as measured clockwise fromthe x 2 axis. Also, as shown in Figure 4.2-3,  is the angle formed by the slip direction and fault
direction, D the magnitude of the slip, and  the strike angle.
The ground is assumed to be Poisson solid (    with the Poisson ratio =1/4).

Appendix 4- 43

x2

δ
h1
W
h2

ξ
x3
Figure 4.2-2 Vertical cross section in the local coordinate system

N

φ
Dd

D

λ

λ
D

Dss

Figure 4.2-3 Definition of fault parameters

Assuming that:
Strike slip
Dip slipDs  D  cos (4.2.2)

Dd  D  sin 

Then for strike slip:   u 1  u i2   u 1  u i3  sin    i 
 cos  dS
u i   D s    i  1 
 1   3    2
(4.2.3)For dip slip:   u 2  u i3   u 2  u i3  sin 2   i 
 cos 2 dS
u i   D d    i   3  2 
    2   3 If the equations (4.2.3) and (4.2.4) are converted to ξ coordinate systems, then for strike slip:

Appendix 4- 44(4.2.4)

u i  D s 

h2

h1

L

   u i1

 u i2   u i1

 u i3 1         sin          cos  d  d 
L



2

1

3

1

(4.2.5)For dip slip:u i  D d 

h2

h1

L

 

 u i3  u i2  u i3

 u i2    2  sin     cos             d  d 
L



2

3



1

(4.2.6)

where,  L  1  L , h1    h2 . The variables are set as given below for integration of equations(4.2.5) and (4.2.6).

 2   cos  3   sin R 2  ( x1   1 ) 2  ( x 2   2 ) 2  ( x 3   3 ) 2 

Q 2  ( x1   1 ) 2  ( x 2   2 ) 2  ( x 3   3 ) 2 
r2  x 2 sin   x 3 cos 
r3  x 2 cos   x 3 sin q 2  x 2 sin   x 3 cos 
q 3   x 2 cos   x 3 sin 


2
2
2
h  q 2  (q3   )

2
2
2

k  ( x1   1 )  q 2(4.2.7)

Also, if the indefinite integral is assumed to be u(1 , ) , then the definite integral is given as:h2

u (1 ,  ) L   u (1 ,  )  u ( L, h2 )  u ( L, h1 )  u ( L, h2 )  u (  L, h1 )
 L  h1

(4.2.8)

If the amount of displacement is directions x1 , x 2 , x3 due to strike slip Ds is U1s ,U 2s ,U 3s and theamount due to dip slip Dd is U1d ,U 2d ,U 3d , the displacement of arbitrary points ( x1 , x2 , x3 ) is given
using the following equations depending upon the pattern of the definite integral across the fault plane.

12
U 1s 
2 r2
4 q 2  2 x 3 cos 
3 tan 4 q 2 x 3 sin   ( x1   1 ) Ds
Q (Q  q3   )Q  x3   3
Q3
 R ( R  r3   )
 4 q 2 q 3 x 3 sin (2 Q  q 3   ) Q 3 (Q  q3   ) 2  ( k  q 2 cos  )( Q  k )  ( q 3   ) k  sin   6 tan 2  tan  1 ( x1   1 )( q 3   ) cos  3 tan  1( x1   1 )( r3   )( x   1 )( q 3   )  3 tan  1 1

r2 R
q2Q


Appendix 4- 45(4.2.9)

12





U 2s 
 sin  3 tan  ･sec  ･  n ( Q  x 3   3 )   n ( R  r3   )  (1  3 tan 2  )  n ( Q  q 3   )Ds

2 x3 ( q 2 cos   q 3 sin  )  q 2 ( q 2  x 2 sin  )2 r2 sin 
2 r cos  2
 2 sin 
R ( R  r3   )R
Q (Q  q3   )2

( x2   2 )( q cos   q 3 sin   x 3 sin 2  )2 2
Q  x3   3Q

 3 tan  4 q 2 x 3 sin 12U 3s 
 cos Ds

( x 2   2 )  q 3 cos    4 q 2 q x sin 2 
Q

2

3

3

3

2Q  q3   Q (Q  q3   ) 2 
3(4.2.10)

 n ( R  r   )  (1  3 tan  ) n (Q  q   )  3 tan  sec  ･  n (Q  x   )
2

3

3

3

3

2 r2 sin ( q  x 2 sin  )2 r2 cos  2 sin  2RQ
R ( R  r3   )2( x3   3 )  q 3 cos  
4 q 2 x 3 sin 2   2( q 2  x 2 sin  )( x 3  q 3 sin  ) 4 q 2 x 3 sin 
Q (Q  q3   )Q 3 sin  4 q 2 q 3 x 3 cos  sin 
212

2Q  q3   Q 3 (Q  q3   ) 2 (4.2.11)(4.2.11)

2 4

U 1d 
 x3
  ( x 2   2 ) sin     4 3 33 DdQQ  x3   3 
R Q x (x   ) ( x  3 )( x  3 )
 cos   3 n ( Q  x3   3 )  2 3
4 3
 4 3 3 33 3 
R
Q
Q


3
 n (Q  x3   3 )  sin  ･  n (Q  q3   )

cos 





 cos q 2 sin  6 x3 



(
)
Q
Q
Q
q


3



12

(4.2.12)
U 2d 
43 x33( x1  1 )
 sin   n( R  x1  1 )  n(Q  x1  1 ) Dd Q (Q  x1  1 ) (Q  x3   3 )
 2Q  x1  1   24
 ( x2   2 ) 2  43 x3  3
2  
 R ( R  x1  1 ) Q (Q  x1  1 )
 Q (Q  x1  1 )    2Q  x1  1  4( x3  3 ) 2( x3  3 )
 cos   ( x2   2 )  43 x3 ( x3  3 )  32  Q (Q  x1  1 )   R ( R  x1  1 ) Q (Q  x1  1 )
 ( x   )( x   )  ( x   )( r   ) 
1  ( x1  1 )( q3   ) 6 tan 1  1 1 2 2   3 tan 1  1 1 3
  6 tan 

(

)(
)



h
x
Q
h
r
R
q
Q
3
3
2
2






 ( k  q2 cos  )(Q  k )  ( q3   ) k sin  
 1
6 
tan 1 ( x1  1 )( q3   ) cos  cos  (sin 2   cos 2  )( q3   )  2q2 cos  sin  ( x1  1 ) sin 2    
 x3  
Q (Q  x1  1 )
Q (Q  q3   )   Appendix 4- 46(4.2.13)12 2Q  x1  1  
U 3d 
4( x3   3 )
 2( x3   3 ) sin   ( x2   2 )  4 3 x3 ( x3   3 )  3
2 
Dd
R
(
R
x

)
Q
(
Q
x

)





1
1
1
1
 Q (Q  x1  1 )   ( x   )( x   2 ) 
1  ( x1  1 )( r3   ) 
1  ( x1  1 )( q3   ) 6 tan 1  1 1 2
  3 tan   6 tan 
(
h
x

)(
Q
h
)
r
R
q
Q
 
2
2




  3 3
4 ( x3   3 ) 2   3 x3
2( x3   3 ) 2
 cos    n ( R  x1  1 )   n (Q  x1  1 ) 
R ( R  x1  1 )
Q (Q  x1  1 )
 2Q  x1  1  
4 3 x3 ( x3   3 ) 2  3
2  Q (Q  x1  1 )   2( q3   )
x1  1(sin 2   cos 2  )  
6 x3  cos  sin    q2Q (Q  x1  1 )  
 Q (Q  x1  1 ) Q (Q  q3   ) 

(4.2.14)

where, displacement u1 , u 2 , u 3 in dirctions x1 , x 2 , x3 is given as:

u1  U 1s  U 1d 
u 2  U 2s  U 2d 
u 3  U 3 s  U 3d (4.2.15)

For the global coordinates (calculation coordinate system), as shown in Figure 4.2-4, the origin is thesame as for the ( x1 , x 2 , x3 ) system. If the X axis takes direction E, the Y axis direction N, and the Z axis
downward and φ (eastern route from the Y axis is positive) is the angle formed by the Y andx1 axes,then the conversion of the amount of displacement (u x , u y , u z ) of the ( X , Y , Z ) system is given
according to the following equation when (u1 , u 2 , u 3 ) is the amount of displacement of the ( x1 , x 2 , x3 )system.

u x  u 1 sin   u 2 cos  u y  u 1 cos   u 2 sin  u z  u3

(4.2.16)

Y(N)

x1

φ
X(E)

x2
Figure 4.2-4 Local coordinate system and the calculation coordinate system
The equation (4.2.14) is the correction given by Okada (1985) of the misprint in the original
Appendix 4- 47

paper by Mansinha and Smylie (1971).
4.2.2. Method using three-dimensional sea bottom movement analysis
In cases where examinations are conducted of tsunami that take into consideration the effectthat three-dimensional underground structures have on tsunami as well as the time change of sea
bottom displacement, a method may be applied that uses analysis of sea bottom movements capableof taking into account three-dimensional heterogeneous underground structures (Tsuchiya et al.,2013). This method is presented below.
4.2.2.1. Three-dimensional sea bottom movement analysis
First, a three-dimensional sea bottom movement analysis is employed to calculate the timechange in ground displacement from a ground motion analysis that takes into consideration threedimensional heterogeneous underground structures.
The National Research Institute for Earth Science and Disaster Resilience’s Ground Motion
Simulator (GMS), which is a tool for ground motion analysis using a three-dimensional finite
differential method, is one of calculation methods of ground motion analysis considering threedimensional heterogeneous underground structures and time change of ground displacement. The timechange in ground displacement may be calculated by a ground motion analysis that uses the earthquake
ground motion analytical tool GMS to take into account three-dimensional heterogeneous
underground structures.
The data on three-dimensional underground structures may be downloaded from, for example the
National Research Institute for Earth Science and Disaster Resilience’s Earthquake Hazard Station.
These data include all land and sea areas around Japan, and may be used for ground motion analysis
that takes into consideration three-dimensional underground structures.
4.2.2.2. Tsunami analysis accounting for time change in sea bottom displacement
A method that sets the time change of ground displacement is shown below.
Continuity equation:

(   ) M N


0
t
x y
where, x, y are horizontal axes, t is time,  is water surface elevation, M, N are discharge fluxes inthe x- and y- directions, and ζ is sea bottom vertical displacement.
Discretization of the above continuity equation gives the following.
Appendix 4- 48

 xt M ik, j 1   ik, j   k 1   k   ik, j   k 1 k 1 / 2
k 1 / 2i 1 / 2, j  M i 1 / 2, j yt Nk 1 / 2
k 1 / 2
i , j 1 / 2  N i , j 1 / 2tt k 1 / 2
M ik11/ /22, j  M ik11/ /22, j 
N i , j 1/ 2  N ik, j 11/ /22
x
y





where, k is number of calculation steps.
In cases where the time change of sea bottom displacement is taken into account, the results ofcalculations of three-dimensional sea bottom movement analyses are used to find the moment-bymoment vertical displacement increase amount Δζ so that this may be given.
4.2.2.3. Case studies of tsunami analyses using three-dimensional sea bottom movement analysis(Tsuchiya et al., 2013)
Case studies of earthquake ground motion analyses, which took into account three-dimensional
heterogeneous underground structures using GMS, as well as case studies of tsunami analyses, whichused these calculation results, are presented below.
(1) Tsunami source model
The target earthquake is the 1923 Kanto earthquake, and the tsunami source model by Aida
(1993) is adopted. The fault plane is represented by a total of 732 point sources (arranged atintervals of 2.5km), the rupture point was configured as 35.3°N and 139.1°E, depth as 11.7km(compiled by the National Astronomical Observatory, 2007), the rupture velocity as 3.0km/s,
hypocenter time function as a triangular pattern, and the rise time for point sources as 4 seconds.
(2) Underground structure model
Three types of underground structure models have been created: the uniform physicalproperties model, horizontal stratification model, and three-dimensional underground structure
model. For the values of physical properties in the uniform physical properties model, ρ was
configured the value by the Central Disaster Management Council (2002), the Q value was thevalue by Sato et al. (1999), Vs was configured using μ=ρVs2 with rigidity μ=4.00×1010N/m2 , andVp was Vp= 3Vs . In addition, the values for the physical properties in the horizontal stratification
model have been configured with reference to Sato et al. (1999). For the values of the physicalproperties in the three-dimensional underground structure model, data on boundary surface anddepth distribution for three layers beginning with the ground surface have been prepared bysynthesizing with Suzuki (2002) as well as Yamada and Yamanaka (2003), and layers from thefourth and later layers from the ground surface have been set with reference to Sato et al. (1999).

Appendix 4- 49

(3) Conditions for calculation of three-dimensional sea bottom movements
The computation region is a range extending 240km east to west and 240km north to southencompassing the tsunami source, and the depth is between 0km and 104km. Of this, thenonreflecting boundary is 24km to the side and 24km downward. The grid size isΔx=Δy=Δz=400m, extending from a depth of 0km to 44km, and Δx=Δy=Δz=1,200m for grid sizes
deeper than 44km. The computation time interval is 0.02 seconds, and the simulating time is up
to 180 seconds after the earthquake occurred.
(4) Results of calculation of three-dimensional sea bottom movements
The final vertical displacement of GMS results was compared with the method proposed by
Mansinha and Smylie (1971), and there was a maximum difference of 15%, excluding points far
from the tsunami source. Also, no clear trends were respect to differences in methods or locations.
In addition, in a time series of vertical displacement in underground structure models asshown in Tsuchiya et al. (2013) Figure-5, areas also emerge where maximum amplitude ofdisplacement is twice that of the final displacement. Moreover, the amplitude increased at thepeak with the horizontal stratification model and three-dimensional underground structure modelin comparison to the uniform physical properties model. When the maximum displacement at
point D is compared, the three-dimensional underground structure model is approximately 1.5
times that of the uniform physical properties model, but the cycle of the displacement waveform
is less than 10 seconds, and the infulense of such displacement on the tsunami will be only in thearea vely close to the wave source region.
However, the cycle of the displacement waveform that occurs here is thought to depend
significantly on the source time function (rise time at point sources), an appropriate configurationneeds to be set in keeping with the target earthquake.
(5) Tsunami calculation conditions and calculation cases
According to the method of Manshinha and Smylie (1971) and the results of analyses andcalculations of three-dimensional sea bottom movements given in (4) sets an initial condition, isgiven to perform tsunami calculations.
The computation region is a range that encompasses the area from the Chiba Prefecture to
Aichi Prefecture. The grid sizes have been subdivided successively (1,600m ~ 800m ~ 400m ~200m ~100m), and the coastline from Chiba Prefecture to Aichi Prefecture used a land run-up
model with a grid size of 50m. Also, the conditions of the offshore boundary were a nonreflecting
boundary. The time interval was set at 0.5 seconds, and the simulating time extended up to six
hours after the earthquake occurred.
Tsunami analyses were performed of a total of five cases: Case 1 which used vertical
Appendix 4- 50

displacement by Mansinha and Smylie (1971), Case 2s which used final vertical displacement in
the GMS results using the uniform physical properties model, Case 2d which used the timechange of vertical displacement in the GMS results using the uniform physical properties model,
Case 3d which used the time change of vertical displacement in the GMS results using thehorizontal stratification model, and Case 4d which used the time change of vertical displacementin the GMS results using the three-dimensional underground structure model.
(6) Tsunami calculation results1) Impact of time change in sea bottom displacement on tsunami
A comparison was conducted of the tsunami results from Case 1, which use the methodof Mansinha and Smylie (1971), as well as Case 2d and Case 2s, which used GMS results
based on the physical properties model, and the impact, which time change in sea bottom
displacement has on the maximum water level of a tsunami, was examined.
From the time series of the water level of Case 1 and Case 2d as well as time series of thesea bottom displacement by GMS result, shown in Tsuchiya et al. (2013) Figure-8, the waterlevel in Case 2d appears to be greater than that in Case 1 at first glance, but the ground itself
has risen, so a tsunami does not necessarily occur that is excessively larger than that in Case 1
immediately after an earthquake occurs. Also, at any points as well, the water level in Case 2dcorresponds to the ground formation immediately after an earthquake occurs, but a significant
difference is no longer seen when compared to Case 1 as the ground deformation converges.
This is because the initial displacement waveform has a 10-second period and there is almost
no contribution to the tsunami, and the long-period wave, which occurs due to the final
displacement distribution, accounts for the principal component of the tsunami. Also, acomparison of the maximum water levels at points along the coastline from Tokyo Bay to
Sagami Bay showed that the maximum water levels at points in Case 2d were at the most 10%
greater than those in Case 1, and, even when compared with Case 2s, the difference was a
maximum of 10% (mean of 5%).
2) Impact of differences in underground structures on tsunami
Comparisons were performed of the results of tsunami calculations from Case 1, which
use the method proposed by Mansinha and Smylie (1971), and Cases 2d, 3d and 4d, which use
the GMS results based upon the three types of underground structure models, to examine theeffect that differences in underground structures have on tsunami.
The results showed that the maximum water levels of the three respective types ofunderground structure models were at the most 15% (mean of 5%) higher than that in Case 1,
and, even when compared with the three types of underground structure models, the maximum
difference was 20% (mean of 5%).
Appendix 4- 51

4.3. Wave front condition, calculation grid size, friction coefficient and coefficient of eddy viscosity
4.3.1. Wave front condition
Moving boundaries need to be configured to represent sea bottom exposure accompanying
tsunami run-up onto land and drawback. The method of Iwasaki and Mano (1979) has been widelyused for the algorithm and discrete format of moving boundaries. This method approximates the
topography in the area of the tsunami head in a stepwise fashion for grid size widths and distinguishes
between whether or not there is water at the stage at each time step in the calculation process. The
specific points are presented below (Figure 4.3.1-1).
• The tsunami head is located at the boundary between the cell in which the sum of the water depth
and maximum still water depth at the cell boundaries (four sides) is positive, and the cell inwhich the sum is either zero or negative.
• The total water depth at the cell boundary for calculating the flow rate per unit width is given as
the sum of the still water depth at the cell boundary and the higher water depth in the twoneighboring cells.
• The flow rate per unit width is estimated using the momentum equation by assuming that the line
connecting the water level of the wave head and the bottom height in the neighboring cell gives
the surface slope to a first-order approximation. When the total water depth is zero or negative,
the flow rate per unit width should be assumed to be zero.
• When the total water depth approaches zero, the advection term is neglected.
hN(i,j+1)●
η(i-1,j)●h(i-1,j)yhM(i,j)●

η(i,j)●
h(i,j)●
hN(i,j)x

η(i-1,j)Water level
Still water depthD(i,j)

Legendi,j：Cell number in direction of x,yη：Water level
h：Still water depth (Addition of the subscript of M and
N is water depth in the boundary.)
D：Total water depth (η+h)
M,N：Discharge flux

η(i,j)

Sea bottom

x direction section in above figure

Figure 4.3.1-1 Iwasaki and Mano (1979)
Appendix 4- 52

Kotani et al. (1998) revised the above calculation method and proposed the following method(Figure 4.3.1-2).
• The total water depth for calculation of the flow rate is the difference between the water level at
the head and the ground height at dry calculation points. In cases where this difference isnegative, the flow rate is zero (no run-up).
• In cases where the total water depth is zero or below a minimum value when calculating theadvection term, only items where the total water depth is the denominator are omitted and theadvection term is calculated.

η(i-1,j)
D(i,j)

Water levelη(i,j)

Sea bottom

The same example as Figure 4.3.1-1

Figure 4.3.1-2 Kotani et al. (1998)
4.3.2. Grid sizes
4.3.2.1. Grid size in the propagation area
If the sea bottom topography is straightforward, the grid size can be 1/20 or less than one
wavelength of a spatial tsunami (Hasegawa et al., 1987), However, it is the complex sea bottom
topography, attention needs to be given to the following and other matters that have been pointed out.
• It is important to accurately express wave refraction in order to improve the precision of tsunami
propagation calculations (Sayama et al., 1986).
• The actual topography is unable to be sufficiently represented using rough grid sizes, andcalculation results will often shift very greatly (Imamura and Li, 1998).
Here, for the actual topography off the coast of Shimoda, the method by Goto is used to conduct
an empirical examination and show the impact that calculation grid sizes for sea areas have on the
maximum water level ascent in the propagation process.
(1) Study sea area and examined tsunami
1) Study sea area
Appendix 4- 53

• The area off the coast of Shimoda, where it is considered difficult to represent refractive
phenomena resulting from the sea bottom topography, is the sea area to be examined.
• The area for which calculations are to be performed is the sea area that is approximately 16km
east to west and 24km north to south extending from near the Izu Peninsula to the northern partof Shimoda City.
2) Examined tsunami
The 1854 Ansei-Tokai earthquake and tsunami will be examined.
(2) Grid sizes and boundary conditions
1) Grid sizes
Uniform grid sizes have been configured for six cases using 50m, 100m, 200m, 400m,
800m, and 1600m.
2) Boundary conditions• Incident wave at open boundary: The results of calculations of the 1854 Ansei-Tokai
earthquake and tsunami using the Ishibashi (1976) model implemented across a wide area areprovided along an open boundary.
• Shoreline: Vertical wall
(3) Comparisons of maximum water level ascent
1) Tsunami propagation route
The tsunami propagation paths, obtained by calculation each grid size, were compared in
Figure 4.3.2-1. The propagation times and propagation paths in cases where the grid sizes wereset at 50m, 400m and 800m are shown in Figure 4.3.2-2 along with the water depths. At theresults, knowledge has been gained such as:• Because of the geographical features of this sea area, tsunami head toward Shimoda City while
going around in the process of propagation, so wave refraction needs to be reproduced withgood precision for accurate calculations.
• Calculation of wave refraction having good accuracy are possible if 400m grids are used forwater depths of 100m and grid sizes ranging from 200 ~ 50m for water depths of 50m or
shallower.
2) Maximum water level ascent along wave direction lines
From the relation between the maximum water level ascent and grid size along the
propagation paths (Figure 4.3.2-3), almost no impact is observed even when grid sizes of 800m
are set for water depths of 100 m or greater, but grid sizes need to be set at 200m or less forwater depths between 50m and 100m, and grid size set at 50m for water depth of 50m or
shallower.
Appendix 4- 54

3) Summary
To obtain a convergence value, it is necessary to select grid sizes on the order of:
Shallow sea areas 100m or deeper : Maximum 800m
Waters depths between 100 ~ 50m : Maximum 200m
Shallow areas of 50m or less

: 100 ~ 50m

Appendix 4- 55

Grid size

Grid size

Computational
regionFigure 4.3.2-1 Comparison of tsunami propagation

Appendix 4- 56

Wave ray
Propagation time(minutes)
Water depth (m)Grid size Δx＝50m

Wave ray
Propagation time(minutes)
Water depth (m)Grid size Δx＝400m

Wave ray
Propagation time(minutes)
Water depth (m)Grid size Δx＝800m
Figure 4.3.2-2 Water depth, propagation time, and propagation path
Appendix 4- 57

Maximum water rize(m)Grid size

Maximum water rize(m)Water depth(m)Maximum water rize(m)Water depth(m)Maximum water rize(m)Water depth(m)Water depth(m)Figure 4.3.2-3 Relation between the maximum water level ascent and grid size along propagation path

Appendix 4- 58

4.3.2.2. Grid size of sea areas around target sites(1) Harbours and ports
Inagaki et al. (2001) analyzed the influence of grid size to the maximum water level ascentinside a ports, such as the facility of the nuclear power plants.
The following characteristics from the results of a comparison of flow patterns andmaximum water level ascent.
• The water level inside a port rises as the grid sizes are greater, and, particularly in cases wherea port or harbor opening is modeled as one grid (Δx=150m), this tendency is pronounced.
• When focusing on current velocity vectors and water level distribution, the smaller the gridsize around the port opening, the more complex the flow patterns become. Futhermore thecharacteristics of the water level distribution are also in harmony with differences in theflow patterns.
• As for the time series of the water level and current velocity in the center of the port opening,the difference when the grid size is set at 75m or less is not that pronounced, but there isclearly a difference in the velocity distribution pattern.
• In the case of the grid size of 25m and 150m phase was a significant difference.
The reason why smaller grid sizes result in lower water levels inside a port appears to bebecause the smaller the grid size is, the more pronounced the vortex at the port opening and theaccompanying dead water region become and the inflow width of the main channel narrows,
inhibiting entry of flow accompanying the tsunami.
Judging from the aforementioned analytical results, even where the grid size per wavelength
satisfies the basic conditions (in this model, where the number of grids per wavelength is 20 evenfor cases where the incident wave period is set at 5 minutes), cases where a comparatively large
grid width is set in comparison to the port opening width are subject to significant constraint in
the flow pattern, so it is desirable to create a model of the area around the harbor using grid sizes
that are 1/5 of the port opening width.
(2) In the case of V-shaped harbours
Noticeably higher run-up height record of historical tsunami have been seen in small Vshaped harbors along deeply indented coastlines in comparison with the surrounding area. At aminimum, detailed grid models need to be used to verity such high water records. Also, adjusting
the run-up height with rough grid mode is to high levels on the records of historical tsunami may
be overestimate the fault slippage, so sea areas where inappropriate grids are used should be
excluded from the area where reproducibility will be assessed.
Within such a background, Inagaki et al. (2001) analyzed the sensitivity of small V-shaped
Appendix 4- 59

harbors where significant tsunami hight is thought to occur, and the following knowledge wasgained with respect to grid partitioning.
The variables indicated below are utilized in arranging the calculation results.
Intra-harbor mean wave length: Lv(=T(gh/2)1/2)

Mean wave length from harbor center to back : Lo(=T(gh/4)1/2)
where, T is incident wave period, g is acceleration of gravity, h is water depth at the harbour
mouth, and λ is distance from harbor mouth to the innermost area, and Δx is spatial grid size.
Characteristics observed in the relationship between grid size and maximum water level ascentare presented below.
1) Distribution of maximum water level rise inside harbors
In most cases, the maximum water level rise inside a harbor tends to be more amplified in
the innermost area than in the center of the harbor, regardless of harbor shape or length of theincident wave. However, in cases where ratio Lv/λ between the intra-harbor mean wave length
Lv and distance λ to the innermost area of the harbor is 20, there is almost no amplification forthe harbor as a whole. In cases where Lv/λ is the same even though the length of the input wave
and the length to the innermost area of the harbor are different (for example, λ=1,000m :T=5min, λ=2,000m : T=10min, λ=4,000m : T=20min), the maximum water level rise is almost
the same when the horizontal distance is made dimensionless.
2) Distribution of maximum water level rise from harbor mouth to center
Within the range of the grid size as configured here, the maximum water level ascent does
not vary significantly, and, if the grid size Δx is set at 1/40 of the intra-harbor mean wave length,
the calculation may be performed within an error of 5% inspite of the value of Lv/λ.
3) Maximum water level rise at the innermost part of the harbor
The maximum water level ascent at the innermost part of the harbor depends significantly
on the relationship between the intra-harbor mean wave length Lv and the distance from theharbor mouth to the innermost part of the harbor.
• In the case of Lv/λ < 6
The incident wave amplifies suddenly at the innermost part of the harbor, and thecalculation results vary greatly depending upon grid size. It is necessary to gradually bring thegrids smaller from the center of harbor and to set a grid size of 1/100 or less of Lo at the
innermost part of the harbor.
• In the case of 6

Lv/λ

10

Although the sudden amplification of the incident wave occurs slightly at the innermost
part of the harbor, if a grid size that is 1/50 of Lo is used, then it is possible to keep calculation
error at around 5%.
Appendix 4- 60

• In the case of 10 ≪ Lv/λThere is gentle amplification of the incident wave, and, if a grid size is utilized that is 1/40
of mean wave length Lo at the innermost area of the harbor from the central area, then thecalculation may be performed such that error is less than 5%.
(3) Run-up area
According to Goto and Shuto (1983), the grid size mean the head of run-up waves is reguired
to satisfy the condition; Δx/αgT2<4×10-4 (Δx is gird size, T is wave period, α is bottom slope)
Here, the range from the shallow sea area to the run-up area is the focus, and a sensitivity analysis
is conducted of the grid size to obtain a guide for error that appears to include the grid size used
for these areas.
1) Governing equations and numerical scheme[1] Governing equations
The following basic equations are used.
• Continuity equation

 M
0

x
t
• Momentum equationMMM   M 2   gD
 ( gn 2 / D1 / 3 )
0
 
x
t x  D 
D2
where, x is spatial coordinates for a static water surface, h is still water depth, D is total
water depth expressed by D=h+η, t is temporal coordinates, g is the gravitational
acceleration, M is flow rate per unit width in the x direction, η is the vertical displacementof water surface above the still water surface, and n: Manning’s coefficient of roughness.
[2] Numerical scheme
The staggered leapfrog method is the basis for the numerical scheme, and the firstorder upwind difference is applied for the advection term.
2) Examination conditions
The examination model is a one-dimensional channel with a uniform depth and a slope inthe edge of channel as shown in Figure 4.3.2-4. The incident wave is given by havingsinusoidal wave at semi-amplitude 2a be the initial tsunami shape, and this initial tsunami
shape propagates as sinusoidal waves of semi-amplitude along the coast and out to sea,
respectively. Also, consideration is given so that there is no noise in the calculation by setting
a sufficient propagation distance towerd offshore.

Appendix 4- 61

Assumption in case of complete
reflection in 5m depth.

Initial wave
(Sinusoidal wave)

2ah=50m ：L= 6,640m(Wave length of period 5 minutes)
h=100m：L= 9,390m( 〃 )Water depth h=50m,
100m, 200m

L

h=200m：L=13,280m( 〃 )Figure 4.3.2-4 Initial wave and target topography
The examination conditions are shown in Table 4.3.2-1. According to Goto and Shuto(1983) when error within 5% is permissible, the grid size at the wave head needs to utilize
Δx=1.27m for a 3-minute period, Δx=3.53m for a 5-minute period, and Δx=14.13m for a 10minute period with respect to the grid size at the wave head. Moreover, in order to obtain asolution that generally coincides with the theoretical solution, it is necessary for the grid size
to be approximately 1/4 grid size described previously when reading from the diagram shown
by Goto and Shuto (1983). Accordingly, the minimum grid sizes were set at 1m for the 3- and5-minute periods, and 2m for the 10-minute period to investigate the sensitivity of therespective grid sizes as the grid size was gradually increased up to 400m. Also, comparisonswere made of cases where these grid sizes were combined to make uneven intervals.

Appendix 4- 62

Table 4.3.2-1 Examination conditions
Items

Contents

Amplitude and waveform of

The sinusoidal wave of the half amplitude 2m is given to theincident wave

offshore boundary as initial wave.

Period T of incident wave

3, 5, 10 minutes

Wavenumber of incident wave

One wave given as initial wave

Slope of sea bottom
Manning’s

coefficient

1/100
of

0.03m-1/3･s

roughness n
1 ~ 400m(T=3,5 minutes)

Grid size Δx

2 ~ 400m(T=10 minutes)3) Results of sensitivity analysis
According to the results of the sensitivity analysis, the knowledge presented below was
obtained. However, the correct solution for the maximum water level rise was a “convergencesolution” for the value where the grid size was gradually reduced and the maximum water levelascent settled at a level that was almost constant. In addition, the convergence solution for thecase of uneven intervals between grids also used this value.
[1] Case of uniform grid size
• If the error of the maximum water level ascent is kept held at about 5%, the grid size forcalculation of wave run-up is reguired to be
16m for a 3-minute period,
20m for a 5-minute period,
25m for a 10-minute period, as shown in Table 4.3.2-2.
• Similarly, if the grid size for a case of complete reflection is a period of 5 minutes ormore is about 200m, then the error will be within 5% even using a grid size of 200m
(Table 4.3.2-3).
• Contrary to Goto and Shuto (1983) which omitted bottom friction, in cases where theroughness coefficient is set at n =0.03m-1/3･s, the grid size may be configured slightly
larger, and, in order to keep error of the maximum water level ascent at about 5%, it issufficient to set the configuration so that grid size Δx is x / gT 2  7 104 (Figure
4.3.2-5).

Appendix 4- 63

Table 4.3.2-2 Ratio to convergence solution of the maximum water level ascent(Offshore depth: 50m, n =0.03m-1/3･s)
Grid sizeΔx (m)

Run-up onto sloping land

Complete reflection

Period Ｔ(minute)
3

5

10

3

5

10

1

1.00

1.00

2
4

1.03
0.99

1.00
0.99

1.00
1.00

1.00

1.00

1.00
1.00

1.00
1.00

8

0.97

0.98

0.99

1.00

1.00

10

0.96

0.98

0.98

1.00

1.00

16

0.95

0.95

0.99

1.00

1.00

20

0.91

0.95

0.98

1.00

1.00

25

0.92

0.94

0.95

1.00

0.99

50
100

0.85
0.78

0.88
0.79

0.92
0.90

1.02
1.03

0.98
0.96

Table 4.3.2-3 The maximum grid size when error of the maximum water level ascent is assumed to be5%(unit(m), n = 0.03 m-1/3s)
Offshore depth(m)Run-up onto sloping land

Complete reflection

Period Ｔ(minute)
3

5

10

3

5

10

50
100

16
20

20
25

25
25

－
－

200
200

200
400

200

25

25

50

－

200

400

Ratio to minimum grid sizeNote) -: The numeric vibration is caused and the evaluation is impossible.

10-4

10-3

10-2
Δx/αgT2

10-1

Figure 4.3.2-5 Relation between ratio to convergence solution of the maximum water rise andparametere (Δx/αgT2) of Goto and Shuto(1983)
Appendix 4- 64

[2] Case of nonuniform grid sizes• For periods of 5 minutes or longer, if an appropriate grid size is selected from the partition
patterns shown in Figure 4.3.2-6, then it is possible to hold calculation error to within 5%(see Table 4.3.2-4).
• In the case of a 3-minute period, in order to kept calculation error within 5%, it is often
necessary to use a finer grid size than that patterns shown in Figure 4.3.2-6 (Table 4.3.24).
Depth

Sea bottom slope: 1/100

Grid size(m)Pattern
Depth

(a)
(b)
(c)

Depth

(d)
(e)
(f)

Depth

(g)
(h)
(i)
(j)
(k)

Figure 4.3.2-6 Grid size pattern of comparative calculation
Table 4.3.2-4 Relation between grid size pattern and the maximum water level ascent
Offshore depth

Grid size(m)

Pattern

50

100

200

Run-up onto sloping land

Complete reflection

Period Ｔ(minute)
3

5

10

3

5

10

(a)

0.87

0.91

0.95

1.00

1.02

0.99

(b)

0.92

0.94

0.97

1.02

1.00

1.00

(c)

0.85

0.88

0.92

0.98

1.02

0.99

(d)

0.93

0.97

0.98

1.00

0.97

0.98

(e)

0.93

0.97

0.98

1.00

1.03

0.99

(f)

0.90

0.94

0.97

0.94

1.05

0.99

(g)

0.99

1.00

1.00

0.92

1.03

0.99

(h)

0.98

0.99

1.00

0.99

1.06

0.99

(i)

0.93

0.98

0.99

0.66

1.02

0.97

(j)

0.96

0.96

0.98

0.81

1.06

1.00

(k)

0.75

0.93

1.00

0.58

0.84

1.04

Appendix 4- 65

4) Energy balance in calculation
The calculation error was estimated by the energy balance in run-up calculation using
uniform grids, when the convergence solution was obtaind. Energy balance error when the
maximum water level ascent emerges is shown below. From these results, the energy balanceerror reaches approximately 10% in the case of a 3-minute period, but it may be observed thaterror will be below 5% even for a 100m spatial grid size with a period of 5 minutes or longer,
and there are no issues present.
Table 4.3.2-5 Energy balance error
Period(minute)3510Grid size(m)Energy balance error
(%)

1

11.3

16

10.6

100

12.8

1

2.4

20

2.8

100

5.0

2

0.9

25

0.8

100

1.1

5) Methods for an exact solution (Nagano et al., 1989)
Using the follow-up approach suggested by Richardson (Fujikawa, 1982), it is possible
to estimate an exact solution for a differential equation from an approximate solution derived
using numerical calculation. However, the exact solution referred to here is the convergencevalue of numerical solutions when grid size approaches the limit of zero.
u represents the exact solution and the approximate solutions for grid sizes Δx1, Δx2, andΔx3 are u1, u2, and u3 respectively. Assuming that the discretization error is proportional to theΔx power, then the equations are expressed as:u  u1  A( x1 ) p
u  u 2  A(  x 2 ) pu  u 3  A(  x3 ) p
and it is sufficient to solve this system of equations to find u. For example, ifx1  x2 / 2  x3 / 4 , then:

Appendix 4- 66

 u  u2 p  log 2  3
 u 2  u1 u

Δx2  p u1  x1  p u 2
x2  p  x1  p

4.3.3. Impact of bottom friction coefficient and vortex viscosity on calculation water level
4.3.3.1. Bottom friction coefficientWith the nonlinear long-wave theory equation, the sea bottom friction term indicates thecomponent for shear force on the sea bottom (τx/ρ, τy/ρ) driven by integration of the vertical vortex
viscosity term into the depth. If the frow is uniform, it is expressed as:

x /  ff
MQ ,  y /   2 NQ
2D
D

where, f is bottom friction coefficient, M and N are component for flow rate per unit width in the x
and y direction, Q is flow rate per unit width, and D is total water depth.
Iwasaki and Mano (1979) introduced the transformation equation f=gn2/D1/3 between friction
coefficient f and Manning’s coefficient of roughness n, and used Manning’s coefficient of roughnessn to express the friction term. Here, the sensitivity of the roughness coefficient is analyzed and theimpact that it has on calculation water level is examined.
(1) Examination conditions
The examination is carried out with one-dimensional water channel having a uniform depth(run-up calculation) (Figure 4.3.2-4). The incident wave is provided by having sinusoidal wave
at semi-amplitude 2a be the initial tsunami shape, and this initial tsunami shape propagates assinusoidal waves of semi-amplitude along the coast and out to sea, respectively. Also,
consideration is given so that there is no noise in the calculation by setting a sufficient propagation
distance out to sea. The principal examination conditions are shown in Table 4.3.3.1-1.

Appendix 4- 67

Initial wave
(Sinusoidal wave)
2a

Water depth h=50m

L=6,640m(Wave length ofperiod 5 minutes)

L

Figure 4.3.3.1-1 Initial wave and target topography
Table 4.3.3.1-1 Examination conditions
Items

Contents

Amplitude andwaveform of incident

The sinusoidal wave of the half amplitude 2m is given to theoffshore boundary as initial wave.

wave
Period T of incident
Wavenumber of incident

5, 10, 20, 30 (minute)wave

One wave given as initial wave

Slope of sea bottom
Grid size ΔxManning’s coefficient ofroughness n

1/10, 1/50, 1/100
22.1359m ( 1/300 of wave length of period 5 minutes )0.0, 0.01, 0.02, 0.03, 0.04, 0.05m-1/3･s(2) Results of comparative calculations
Tables 4.3.3.1-2 and 4.3.3.1-3 show comparisons of the maximum water level ascent anddescent for cases where Manning’s coefficient of roughness was varied. Also, Figure 4.3.3.1-2
shows the distribution of maximum water level ascent and descent for a case where the sea bottom
slope incline was set at 1/100. From the results of these comparative calculations, characteristics
have been summarized and presented below.
• In a case where the sea bottom slope is set at 1/10, even if roughness coefficient n is varied
between 0 and 0.05, the change in the maximum water level ascent and descent is limited toa maximum of approximately 9%.
• In a case where the sea bottom slope is set at 1/50 when the periods for the incident wave are
Appendix 4- 68

5 minutes and 10 minutes and in a case where the sea bottom slope is set at 1/100 when the
periods for the incident wave are 5 minutes, 10 minutes and 20 minutes, a variance is yieldedof close to a maximum of 50% in sea areas having a depth of 10m or shallower.
Table 4.3.3.1-2 Comparison of maximum water level rise and fallSeabottom
slope

1/10

1/50

1/100

Manning’s
coefficient ofroughnessn(m-1/3･s)
0.00
0.01
0.02
0.03
0.04
0.05
0.00
0.01
0.02
0.03
0.04
0.05
0.00
0.01
0.02
0.03
0.04
0.05

Period T and maximum water level ascent and descent (m)T=5 minutes
T=10 minutes
T=20 minutes
T=30 minutes
Ascent

2.45
2.45
2.45
2.44
2.43
2.42
4.77
4.60
4.21
3.84
3.49
3.33
5.27
4.66
3.79
3.18
2.74
2.44

Descent

-2.23
-2.23
-2.22
-2.21
-2.20
-2.17
-4.71
-4.63
-4.28
-4.11
-3.58
-3.25
-4.39
-3.85
-3.23
-2.77
-2.42
-2.14

Ascent

2.01
2.01
2.01
2.01
2.01
2.01
3.65
3.48
3.46
3.42
3.36
3.27
4.88
4.48
4.00
3.57
3.17
2.91

Descent

-2.09
-2.09
-2.08
-2.06
-2.03
-2.00
-3.40
-3.39
-3.38
-3.35
-3.30
-3.10
-4.83
-4.66
-4.09
-3.56
-3.13
-2.80

Appendix 4- 69

Ascent

2.01
2.01
2.01
2.01
2.01
2.00
2.53
2.53
2.52
2.52
2.52
2.52
3.56
3.55
3.37
3.33
3.12
2.91

Descent

-2.01
-2.01
-1.99
-1.97
-1.94
-1.89
-2.41
-2.40
-2.37
-2.16
-2.13
-2.10
-3.50
-3.49
-3.47
-3.40
-3.21
-2.97

Ascent

2.01
2.01
2.01
2.01
2.00
2.00
2.42
2.42
2.42
2.41
2.41
2.39
2.92
2.92
2.92
2.91
2.89
2.69

Descent

-2.01
-2.00
-1.98
-1.94
-1.89
-1.84
-2.09
-2.08
-2.06
-2.04
-2.02
-2.00
-2.55
-2.55
-2.53
-2.42
-2.38
-2.34

Maximumwater levelascent(m)Maximumwater level
descent(m)Sea bottom slope 1/100
Period 5 minutes
Incident wave height 1m
Offshore depth 50m

Maximumwater levelascent(m)Distance (m)Maximumwater level
descent(m)Sea bottom slope 1/100
Period 5 minutes
Incident wave height 1m
Offshore depth 50m

Maximumwater levelascent(m)Distance (m)Sea bottom slope 1/100
Period 5 minutes
Incident wave height 1m
Offshore depth 50m

Maximumwater level
descent(m)(n：m-1/3s)
Distance (m)Figure 4.3.3.1-2 Comparison of the maximum water level ascent and descent by difference ofManning’s coefficient of roughness

Appendix 4- 70

4.3.3.2. Eddy viscosity coefficientWith respect to a horizontal eddy viscosity term, there are many cases where the position is takenthat a sufficiently precise solution may be obtained even if it is disregarded, provided that the tsunami
water level is the principal object (Shuto, 1986). However, examples have also been seen where
simulations have been performed that take this term into account in the basic equation (see for example
Tanaka, 1985 and Shibaki, 1994). Also, based upon recognitions such as:• The impact of the eddy viscosity term needs to be examined using a numerical calculation
scheme and set so that it is indicated in the numerical calculation scheme and truncated error
terms.
• The impact of the eddy viscosity needs to be examined with respect to plane issues.
Comparative calculations have been carried out of the impact that the eddy viscosity coefficient
has on calculation water level, and the knowledge gained is given below.
(1) Examination conditions
The principal examination conditions are given in Table 4.3.3.2-1.
Table 4.3.3.2-1 Examination conditions
Items

Contents

Topography

Harbor shown in Figure 4.3.3.2-1 is assumed.

Computational region

Direction of cross shore : 3,000m, Direction of shoreline : 6,000m

Water depth

10m (Uniformity)

Grid size

25m (50, 75, 150m partially was used referring.)

Amplitude and waveform of

The sinusoidal wave of the half amplitude 2m is given to the offshore

incident wave

boundary as initial wave.

Period of incident wave

5, 10, 20 minutes

Direction of incident
wave
Eddy viscosity coefficientManning’s coefficientof roughness
Boundary conditions

Cross to the shoreline
0.0 ~ 102m2/s

n: 0.03m-1/3s
Land/breakwater : Complete reflection, Offshoreboundary : Openboundary

Appendix 4- 71

Shoreline

Water depth 10m
The shape of the breakwater in the cell was matchedto the approximation with maximum grid size
150m.

Width of haber

Figure 4.3.3.2-1 Shape of the breakwater(2) Results of comparative calculations
1) Impact of eddy viscosity coefficient on maximum water level ascent (Figure 4.3.3.2-2)• With a eddy viscosity coefficient of 1m2/s or less, almost no impact has been observed on the
maximum water level ascent due to differences in the eddy viscosity coefficient.
• When the grid size is varied, the level of the absolute value of the maximum water levelascent changes, and the impact due to the eddy viscosity coefficient shows the sametendency.
• The maximum water level ascent is 5 to 10% lower in a case where the eddy viscosity is
0.0m2/s than when it is 10m2/s, and is becomes significantly lower when it is 102m2/s.
• The extent of the impact of the eddy viscosity coefficient differs depending upon the order ofcurrent velocity, geomorphic change, calculation scheme and other factors, so any
generalization is difficult, but the maximum water level ascent is lower at 10m2/s or greater
according to the scales of the models shown here.

Appendix 4- 72

A : Period 5 minutes

A : Period 20 minutes
Ratio of maximum water rize

Ratio of maximum water rize

Ratio of maximum water rize

A : Period 10 minutes(Horizontal axis unit m2/s)

Coefficient of eddy viscosity

Coefficient of eddy viscosity

B : Period 20 minutes

Ratio of maximum water rize

Ratio of maximum water rize

B : Period 10 minutes

B : Period 5 minutes
Ratio of maximum water rize

Coefficient of eddy viscosity

Grid size :C : Period 20 minutes
Ratio of maximum water rize

Coefficient of eddy viscosity

C : Period 10 minutes
Ratio of maximum water rize

Coefficient of eddy viscosity

C : Period 5 minutes
Ratio of maximum water rize

Coefficient of eddy viscosity

Output position

C
B
A

Coefficient of eddy viscosity

Coefficient of eddy viscosity

Coefficient of eddy viscosity

Figure 4.3.3.2-2 Comparison of the maximum water level ascent based on the case of grid size 25m
and eddy viscosity coefficient 0.0m2/s2) Impact of eddy viscosity coefficient on flow pattern (Figures 4.3.3.2-3 and 4.3.3.2-4)• Almost no difference is observed in the flow pattern with a eddy viscosity coefficient of
10m2/s or less, and the circling drift disappears at the harbor mouth at 102m2/s.
• When focusing on the absolute value of the current velocity in the central part of the harbormouth, similarly, almost no difference is observed with a eddy viscosity coefficient of
10m2/s or less, but, at 102m2/s, the current velocity value decreases substantially and theflow direction also changes.

Appendix 4- 73

Grid size

Grid size 25m
Coefficient 0.0m2/s

Coefficient of eddy viscosity
0 m2/s
10 m2/s
102m2/sA

Water level(m)Grid size 50m
Coefficient 0.0m2/s

Grid size 25m
Coefficient 10.0m2/s

Velocity (m/s)

Grid size 50m
Coefficient 10.0m2/s

Flow direction

minutesminutes

Grid size

Coefficient of eddy viscosity
0 m2/s
10 m2/s
102m2/sA

Grid size 25m
Coefficient 102m2/s
Water level(m)Grid size 50m
Coefficient 102m2/s

viscousity and flow
pattern(Period 5 minutes)

Velocity (m/s)

Figure 4.3.3.2-3 Coefficient of eddy

Flow direction

minutesminutesFigure 4.3.3.2-4 Water level, flow direction,
velocity in output position
A (Period 5 minutes)

Appendix 4- 74

4.4. Numerical method for tsunami generated by submarine landslides, slope failure and flank collapse
4.4.1. Overviews of the numerical methods and examples of applications
This section presents overviews of numerical methods for tsunami occurrence along withsubmarine landslides, slope failures and flank collapses and examples of applications.
Not all of the methods described in this section are currently usable. As new methods are proposedin the future, available ones should be investigated again when numerical simulation of tsunami is
performed.
4.4.1.1. Flow rate model(1) Overview
In the flow rate model, the inflow of sediment from land into the sea is treated as that ofwater. At the boundary where sediment flows in, a tsunami is caused by setting flow rate that varyover time. The flow rate is given by:q  Qm l  y / l sint /    Q sint /   , 0  t   ,  l  y  lWhere y is taken along the coastline, ± l for the range of inflow, and τ for the duration. Qm
is the maximum flow rate in the central part of the inflow, and q is the flow rate at position y.
(2) Examples
Aida (1975) applied this method to the 1792 Shimabara flank collapse. For the unit lengthof the coastline, a maximum flow rate of 18,000m3/min is given for a period between 2 and 4
minutes. When the duration of the inflow is 2 minutes, this corresponds to 4.6×107m3 for the total
inflow.
4.4.1.2. Circular slip failure method(1) Overview
The circular slip failure method deduces the topography before and after a landslide on an
unstable slope, and reflects the topography in the water level of the sea surface. Direct lines areconnected so that depressions are covered where traces of landslides are presumed as deduced
from charts showing the submarine topography. The connected lines are set as a cross-section of
the sea bottom before a virtual landslide, and the circular arc slip method is used to perform
calculations of the stability of the slope. Cases, in which the safety factor is less than one and thecomputer cross-section coincides for the most part with a cross-section deduced from current
Appendix 4- 75

traces of submarine landslides, are regarded as cross-sections of landslides to be incorporated
into tsunami analysis. Sediment, which has moved along a slope as a submarine landslide has
occurred, is deposited below the slope, and the mass of the sediment is incorporated into thetsunami analysis in a form where it is preserved. A tsunami is caused as a change in the water
surface occurs that is similar to the change in the seabed due to movement of sediment. With
respect to a direction perpendicular to the direction of the landslide, a cross-section is provided
using the COS function so that the volume of the landslide decreases toward both ends. To
configure the motion of the landslide, the period of time for the landslide is introduced beginningfrom when landslide occurs until the movement of the landslide is completed. The volume of thelandslide sediment, which is estimated using the circular arc slip method, is regarded as anintegral value of landslides that have occurred multiple times and is used by multiplying by afactor of 1 or less.
(2) Examples
Hiraishi et al. (2001) apply this method to the Meiwa Yaeyama tsunami, assuming thesimultaneous occurrence of fault motion and landslide. Provisional calculations are needed forsetting the landslide time, and, in the calculations performed by Hiraishi et al. (2001), three values
were set: 30, 60 and 90 seconds. A range of 0.2 to 1.0 times has been provided for the landslidevolume factor with reference to previous values estimating the number of times landslides haveoccurred.
4.4.1.3. Kinematic landslide model(1) Overview
The kinematic landslide model (KLS) was proposed by Satake and Kato (2002). The modelutilizes detailed topography changes obtained from bathymetric surveys. Displacements at eachpoint are assumed to occur during rise time T. Moreover, this change is regarded as moving fromthe top of the landslide body at propagation velocity U (Satake and Kato, 2002). The evolutionof topographic variations, which are obtained using this method, are taken into consideration ina mass conservation expression as change in the water depth. Propagation velocity U and risetime T are parameters that are analogous to the failure propagation velocity and rise time of theearthquake fault model.
The approaches to propagation velocity are the case where the vertical direction component
Uz is provided (Satake and Kato, 2001; Satake and Kato, 2002; Satake et al., 2002) and casewhere the horizontal direction component U is provided (Satake, 2007).
In the model described above, the slide (missing volume) first appears, then the deposit
Appendix 4- 76

(additional volume) results. Tonomo et al. (2015) focused on this point and proposed a model inwhich collapse and sedimentation proceed simultaneously.
Satake (2007) varied propagation velocity U in a horizontal direction within a range of10~100m/s, referencing the configuration in examinations of observations and past occurrences,in a case study involving a numerical simulation of the 1741 Kanpo tsunami. Also, with respect
to rise time T, Satake (2007) also discussed the difficulty of estimating using propagation velocity
U, and set it to within a range from 1 to 5 minutes.
(2) Examples
Table 4.4.1-1 shows parameters in the case studies where the KLS model is applied totsunami originating in submarine landslides, flank collapses and slope failures.
Table 4.4.1-1Parameters for KLS model in the previous studies*1 Uz=20m/s for Satake and Kato (2002)
Parameter
Events(Reference)
Submarine landslides around
Hawaii(Satake et al., 2002)
1741 Kampo tsunami(Satake and Kato, 2001;
Satake and Kato, 2002)
1741 Kampo tsunami(Satake,2007)

U (Uz)
(m/s)

T
(min)

U = 20,50,100

5Uz = 2,5,10,20*1

1, 2, 5

U = 10, 20, 40, 50, 60,
80, 100

1, 2, 5Note

The observed values are best
explained for the combinationof Uz=10m/s and T=2min.
The observed values are best
explained for the combinationof U=40m/s and T=2min.

4.4.1.4. Landslide motion analysis model(1) Overview
This method gives the movement of landslide sediment, which is obtained using thelandslide analysis model, as sea surface fluctuation for the tsunami analysis model. The
movement of landslide sediment is analyzed using either plane two-dimensional or threedimensional models such as LSFLOW, TITAN2D or FLOW3D. The tsunamis are caused bygiving changes in the thickness of landslide sediment, which are obtained from the results ofanalysis of landslide movement, as a time-series sea surface fluctuation.
Sasahara (2004) combined the Public Works Research Institute’s quasi-three-dimensionallandslide motion analysis program LSFLOW and program for computing fluid flow using a longwave equation, and then analyzed the tsunami that resulted from the 1792 Shimabara sector
collapse. The calculation component of the continuity equation has been revised to address time
variation for layer thickness of landslide sediment.
Appendix 4- 77

(2) Examples
In the case study by Sasahara (2004) applying the model to the tsunami accompanying the1792 Shimabara sector collapse, the acceleration, duration, period and other characteristics of theearthquake are given in order to analyze landslide motion using the LSFLOW model. Also, thephysical properties for the ground have been set using such values as 2.0t/m3 for density, 0.2~0.7°
as the friction angle for the sliding surface (underwater), and 9.0~23° as the angle of internal
resistance.
4.4.1.5. Two-layer flow model(1) Overview
The two-layer flow model was proposed by Imamura and Imteaz (1995) as a basic equation
for the motion of fluids where the density differs in two-layers, the upper and lower.
Matsumoto et al. (1998) enhanced the two-layer flow model developed by Imamura and
Imteaz (1995) to apply it to tsunami occurring due to debris flow. Specifically, terms were added
to the basic equation for expressing bottom friction force, interfacial shear force, and form dragat the head of the debris flow in the sea area. Also, an artificial viscosity term was introduced tosuppress vibration that occurs when the debris flow plunges into the sea. The interfacial resistancecoefficient f inter was introduced for the term expressing interfacial shear force, and the dragcoefficient C D was introduced for the term expressing form drag at the head of the debris flow.
The proposed two-layer flow model has been applied to simulation of hydraulic modelexperiments with hydraulic models as well as past tsunami (1741 Kampo tsunami).
Hashi and Imamura (2000) applied the two-layer flow model to the 1998 Papua New Guinea
tsunami, and examined the position and magnitude of landslides for cases where submarine
landslides are taken into consideration as a factor causing the tsunami.
Imamura et al. (2001) conducted hydraulic model experiments of debris flow plunges in a
one-dimensional water route, and used the two-layer flow model to perform simulation
calculations. The Manning roughness formula has been used in expressions of bottom friction
force. Also, this experiment did not take into consideration form drag based on a determinationthat the head of the debris flow was not in a form that would give rise to significant resistance.
In this research, parametric studies were conducted that varied bottom roughness within a rangeof 0.08~0.12m-1/3s, the diffusion coefficient for the sediment layer within a range of
0.005~0.01m2/s, and the interfacial resistance coefficient within a range of 0~1.0. Based on the
results of a comparison of the results of measurements using hydraulic model experiments andthose of simulation calculations, the optimum combination for this case study was found to be a
Appendix 4- 78

bottom friction coefficient of 0.12m-1/3s and a horizontal eddy viscosity coefficient of 0.01m2/s.
Kawamata et al. (2005) used the two-layer flow model to perform simulations of hydraulicmodel experiments and past tsunami (1741 Kanpo tsunami). The hydraulic model experiments
were carried out using a configuration that was the same as that set by Imamura et al. (2001). The
most appropriate value pairs were proposed as a result of trials of several settings for parameters
included in the two-layer flow model. More precisely, the optimum values were a combination
where the bottom Manning’s roughness coefficient in the air was 0.01m-1/3s, the horizontal eddy
viscosity coefficient was 0.01m2/s, the bottom Manning’s roughness coefficient in the water was
0.012m-1/3s, CD = 10, finter = 0.2, and the duration of the force of interaction was 0.37 seconds.
Multiple calculations were performed for a calculation of the 1741 Kanpo tsunami using differingbottom roughnesses. When the bottom Manning’s roughness coefficient in the air and in the water
was 0.4m-1/3s, the results best coincided with the traces marking the height of the tsunami. The
other settings were 0.1m2/s for the horizontal eddy viscosity coefficient, for the bottom
Manning’s roughness coefficient in the water 0.4m-1/3s, and CD = 2.0. Based upon an analysis of
the results of this simulation, it has been pointed out that there is a strong directivity toward a
direction in which the debris flow traveled (northward), and the reproducibility in this northward
direction is not necessarily good in comparison to the Japan Sea as a whole.
Maeno and Imamura (2007) conducted a study of tsunami during the formation of the Kikai
Caldera approximately 7,300 years ago. The study used tsunami that occurred due to pyroclastic
flow, which accompanied eruption when the caldera was formed, that plunged into the sea, andused the two-layer flow model to perform calculations of the motion of the pyroclastic flow andtsunami. The horizontal eddy viscosity coefficient and interfacial resistance coefficient were set
at 0.01m²/s and 0.2, respectively, based upon Matsumoto et al. (1998) and Kawamata et al. (2005).
Manning’s roughness coefficient for the bottom was set at 0.01m-1/3s for the air and 0.08m-1/3s
for water based upon a comparison of the results of experiments that focused on pyroclastic flowby McLeod et al. (1999) and the results of numerical simulations performed in this study. Formdrag was not taken into consideration.
Maeno and Imamura (2011) applied the two-layer flow model to the tsunami triggered by
the pyroclastic flow following eruption of Krakatoa in 1883. This study examined both cases
where the density of the pyroclastic flow was greater than that of water and where it was less thanthat of water, and applied basic equations that differed according to the respective case.
Manning’s roughness coefficient for the bottom did not depend on the density of the pyroclastic
flow, and was set at 0.01 ~ 0.06m-1/3s for when in the air, and 0.06 ~ 0.08m-1/3s for when in thewater. The values of 0.06, 0.18 or 0.20 were given for the interfacial resistance coefficient. The
horizontal eddy viscosity coefficient was given according to an expression dependent upon the
thickness of water or the pyroclastic flow, the velocity of the pyroclastic flow, and other elements.
Appendix 4- 79

The coefficient β of the viscosity term to suppress numerical vibration was set at 1.2. Formdrag was not taken into consideration.
Yanagisawa et al. (2014) applied the two-layer flow model to the tsunami in the Ariake Sea,
which originated in the sector collapse of Mt. Mayuyama in 1792. This study increased theprecision of landslide calculations by taking a soil parameter into account in the basic equation
for the sediment layer. More specifically, the study applied the law of friction using Coulomb’s
equation and the coefficient of earth pressure generally utilized in numerical models of landslides
and debris flow. Also, to stabilize the calculation, the outflow rate was limited with respect tomesh for which clod thickness was negative. Horizontal eddy viscosity and form drag were nottaken into consideration.
As described above, multiple basic equations have been proposed which differ in theirtreatment of bottom friction force and the force of interaction between seawater and sedimentlayers. Here, a description is given of the basic equation presented by Maeno and Imamura (2007)
as one formulation*. The basic equation for the upper layer (seawater layer) is expressed as:  1   2   M 1  N 1


0
t
x
y

M1   M12    M1N1    gD1 1  INTFx  0 x
t x  D1  y  D1 

N1   M1N1    N12   gD1 1  INTFx  0  t x  D1  y  D1 yThe basic equation for the lower layer (sediment layer) is expressed as:
 2 M 2 N 2


0
t
x
y
M 2   M 22    M 2 N 2 h  
 D     gD2  1  2    x  INTFx  DIFFx tx  D2  y  D2 x x   2
 x D 
N 2   M 2 N 2    N 22 h      gD2   1  2    y  INTFy  DIFFy tx  D2  y  D2 y y   2
 y*Partial supplementation and revisions have been made in comparison with the descriptions
given of the basic equations in other literature.
where, the subscripts 1 and 2 represent the upper and lower layers, respectively.  1 is the waterlevel of the upper layer and  2 the thickness of the lower layer.

h is the still water depth of

the upper layer, D1 the total water depth (= h   1 ), and D 2 the thickness of the lower layer. M
and N are the flow rates per unit width in the x and y directions, respectively.  1 is the densityof the upper layer,  2 the density of the lower layer, α the density ratio (  1 /  2 ), and  / 2 thebottom friction term for the lower layer. INTF indicates the interfacial resistance force andAppendix 4- 80

DIFF the horizontal diffusion term. The bottom friction term, interfacial resistance force andhorizontal diffusion term are expressed as:

x
gn 2

M

D 7 /3M 2  N2 ,ygn 2 7/3 N M 2  N 2
D

INTF x  f inter u u 2  v 2 , INTF y  f inter v u 2  v 2

 2N 2N   2M2M 
 , DIFFy    2 
DIFF x   

2
2 
y 
y 2 
 x
 x

where, n is Manning’s roughness coefficient for bottom friction. f inter indicates the interfacial
resistance coefficient, u, v

the interlayer relative velocities in the x and y directions,

respectively, and ν the horizontal diffusion coefficient.
To suppress the vibration that occurs when debris flow plunges into the sea, the artificial
viscosity term, which is shown below, is introduced into the mass conservation expression.
 x 3where, g  2  2D x 2 x 2

is a constant.

(2) Examples
Table 4.4.1-2 shows parameters in the case studies where the two-layer flow model has been
applied to tsunami originating in submarine landslides, sector collapses and slope failures.

Appendix 4- 81

Table 4.4.1-2 Parameters in two-layer flow model in the previous studies

Event(Reference)
1998 Papua New Guinea
Tsunami(Tachibana and Imamura, 2000)

n(m-1/3s)--- : not described, *: Basic equations are not described
ParameterNote
f interCD(m2/s)----

Parameters
andbasic equations are
not described in thepaper

1741 Kampo tsunami(Matsumoto et al.,1998)-

1741 Kampo tsunami(Kawamata et al.,2005)
1792
Unzen-Mayuyama
landslide tsunami(Yanagisawa et al.,2014)
Hydraulic model experiment for
Tsunami(Imamura et al.,2001)
Hydraulic model experiment for
Tsunami(Kawamata et al.,2005)

-

-

0.25,
0.4,
0.6

*

0.025

2.0

3.0

Assumptionofdilatant fluid leads
to bottom friction
coefficient in the
paper

0.1

0.0

2.0

*

The best fit was
obtained for n=0.4.

-

0.08,
0.10,
0.12

0.005,
0.01,
0.02,
0.03

0.01,
0.05,
0.10,
0.20
0.0,
0.05,
0.20,
1.00

-

Air:0.01
Water:0.12

0.01

0.2

-

*

*

*

*

*

*

10

*

The lower bottom
friction is computed
using
friction
Coulomb’s theory
The best fit was
obtained for the
combinationof
n=0.12 and ν=0.01.

4.4.1.6. Methods for estimating initial water level(1) Overview
Grilli and Watts (2005) and Watts et al. (2005) proposed methods that assess the initial waterlevel distribution of tsunami generated by submarine landslides. Submarine landslides can beclassified as slides and slumps with different equations proposed. With respect to the estimation
equation for initial water level distribution, equations have been proposed for estimating
amplitude and wavelength in cases where the landslide is a two-dimensional cross-section.
Moreover, an equation has been proposed for estimating the distribution of the amount of waterlevel fluctuation in a case where the landslide movement is three-dimensional based upon its
amplitude and wavelength.
The equation for estimating amplitude when the landslide is a two-dimensional cross-section
has been computed by approximating multiple numerical solutions in a functional form that isbased upon theoretical consideration.
The tsunami amplitude and wavelength for slides are given below.

Appendix 4- 82

1.25

 T  b sin  b  d 

o,2D  So (0.0574 0.0431sin ) 

1  e2.2( 1) o  t o gd
Where, 0,2 D is the maximum water level fall immediately above the initial position of thelandslide, S 0 the characteristic distance, T the maximum thickness of the landslide, b thelength when the cross-sectional shape of the movement of the landslide is approximated using a
Gaussian distribution,  the slope incline, d the initial submergence depth of the landslide, the underwater relative density of the landslide, and t 0 the characteristic time. A series ofequations for computing S 0 and t 0 have been proposed as shown below.
So 
ut 

ut2
u
, t0  t ,
ao
ao

gd

B sin   (  1) tan 
1 
,
d
2Cd 
tan     1  tan 1 ao  g sin  tan     Cm 

where, u t is the final velocity, a o the initial acceleration, g the acceleration of gravity, B
the length when the landslide is elliptically approximated, C d the drag coefficient, Cm theadditional mass coefficient, and 

the angle of friction. In addition, Cd  1 , Cm  1 , and  0 have been proposed as appropriate values obtained from experiments. The scope of

applicability for this estimation equation has been given as coinciding with the scope of thecalculation conditions for numerical experiments used when finding approximate equations. In
other words,   [5,30] ,d / b  [0.06,1.5] ,T / b  [0.008,0.2] ,R / b  [1,2] , and  [1.46 ,2.93] .
The amplitude and wavelength for slumps are given below.
1.25

 0.131 T  b sin    sin   b  d 

 o, 2 D  S o 

b
 
 R

0.63

0.39 (1.47  0.35(  1))(  1)

 o  t o gd
where, R is the radius of curvature, and  the rotation angle. In modeling, S o is half ofthe distance until the landslide stops. A case study gives the value for half of the distance overwhich the landslide moves. The following have been proposed as equations for computing R , , and t 0 .

R  b 2 /(8T ) or R  b ,  2 S o / R ,Appendix 4- 83

t0 

R   Cmg  1

In addition, C d  0 and C m  1 have been proposed. The application scopes are  [10,30] ,d / b  [0.34,0.5] ,T / b  [ 0 . 10 , 0 . 15 ] ,R / b  [1, 2 ]  [ 0 .1,0 .52 ]

,

,

and

  [1 .46 , 2 .93 ] .
The following equation has been proposed for estimating the distribution of the water level
fluctuation in a case where the landslide phenomenon is three-dimensional, which is based on
amplitude and wavelength in a case where the landslide phenomenon is a two-dimensional crosssection. First, amplitude  0 , 3 D , which is directly above the landslide term in a case where thelandslide phenomenon is three-dimensional, is given as:


w 


 w  0 

0,3D 0,2D 
where,

w is the width of the landslide. Next, most of the tsunami energy at the t  t0 stage ispotential energy, and a double Gaussian distribution is used for the water level distribution in thiscase, which may be expressed as follows.
  x  x  
  x  x  x   
 0,3 D y  y 0 
00 exp      ' exp   
sec h   x, y  

  

 

w
 min


0 
0
0

 
 
 
 
2





2







where,  min is the minimum value for the right-hand side excluding amplitude,

 theparameter yielding the shape of the distribution in a direction perpendicular to the direction of
the landslide movement, x g the coordinates for the initial position of the landslide, x theparameters governing the distance between the peaks of the rise and fall, x 0 the coordinates ofx0  x g  x , y 0 the coordinate of the landslide position in the y direction.   is theparameter governing the ratio of the positive and negative peaks, but the determination method
is not indicated.
(2) Examples
Watts et al. (2005) applied the proposed formulas to the estimation of several tsunamis fromprevious case studies. The parameters used in the previous studies are given in Table 4.4.1-3.

Appendix 4- 84

Table 4.4.1-3 Parameters for Watts et al. (2005) in the previous studies* : S 0 is not used in slide type
Configuration
Event

Type



T

b

w

2 S0

d



(-)

(m)

(m)

(m)

(m)

(m)

(degree)1998 Papua New Guinea

slump

1.85

760

4,500

4,500

766

1,200

12

1994 Skagway, Alaska

slide

1.85

15-20

180-600

340-390*24-150

9-24

1999 Izmit Bay

slump

1.85

500

5,000

5,000

230

218

5

1946 Unimak, Alaska

slump

1.85

400

40,00025,000358,000

1,600

4.3

4.4.1.7. Distinct element method(1) Overview
A method has been proposed that addresses landslide (solid phase) and seawater (fluid
phase) respectively with the distinct element method and the particle method, and takes into
consideration the interaction between both phases to calculate landslide tsunami. Goto et al.
(2011) proposed a solid-liquid two-phase flow model for application to flank collapse tsunami.
(2) Examples
Goto et al. (2011) used the proposed model to reproduce hydraulic model experiments
simulating flank collapse tsunami, and reported on the basis of the results that the height andother characteristics of tsunami that occurred as well as the motion process from plunge of theparticle group through sedimentation corresponded well overall with the empirical results.
4.4.2. Examination of appropriate grid size
In this section, the two-layer flow model and the KLS model are addressed, and an examination
conducted of the appropriate grid size when performing calculations using both models. For thisexamination, a virtual topography is to be prepared that illustrates submarine landslides, slope failures
and flank collapses, and both models will be applied.
4.4.2.1. Illustration of landslide body
The formula set forth by Lynett and Liu (2005) was adopted to illustrate the formation of landslide
body.

Appendix 4- 85

4.4.2.2. Examination of tsunami originating in submarine landslides(1) Calculation conditions
1) Topographical conditions
Figure 4.4.2-1 shows a topography for a submarine landslide. The flat shallow area ofwater depth Hf and the flat deep area of water depth Hb are connected with the inclining slope

θ, and the landslide body is arranged on this inclination. The length of the inclination is twice
the initial length of the landslide body. For the final depositional landform, the KLS modelyields a distribution that moved in a horizontal direction only in a distance equivalent to length

L of the landslide body from the initial position of the landslide body (zone of depletion). These
parameters have been compiled and given in Table 4.4.2-1.

Appendix 4- 86

Figure 4.4.2-1 Model for submarine landslide
Table 4.4.2-1 Parameters for submarine landslide
ParameterValueΔh (m)
Hf (m)Hb (m)θ (°)κ (= lF/lB)
L (m)
W (m)
γ (= ρs/ρwater )
b

30
500
Hf + 2Ltanθ
3, 6, 12
1.0
600
600
1.85
0.5L

2) Other conditions
The grid size is based on landslide length L, and set at L/40, L/20, L/10, and L/5 (=15, 30,
60, and 120m). The appropriate grid size is examined by comparing solutions obtained using
different grid sizes. Tables 4.4.2-2 and 4.4.2-3 show the other calculation conditions.

Appendix 4- 87

Table 4.4.2-2 Calculation conditions (Submarine landslide)
Parameter

Value

Grid sizes (m)Computation time interval (s)Manning’s roughness coefficient between waterand bottom (m-1/3s)
Kinematic viscosity for water (m2/s)

15,30,60,120
0.05

Calculation method

0.03
10.0
Tanaka(1985)’s
methodTable 4.4.2-3 Calculation conditions for each model (Submarine landslide)
Model
Twolayer
flow
model
KLS
model

Parameter

Manning’s roughness coefficient for lower
layer (soil layer)
Kinematic viscosity for lower layer (soillayer)
resistance coefficient

SymbolValuen (m-1/3s)

0.2, 0.3, 0.4

ν(m2/s)0.01

CD ( - )0coefficient for interface resistance force

finter ( - )0

Horizontal slide velocity

U (m/s)10, 20, 40

Rise timeT (s)120, 240, 480(2) Results
First, the results of the two-layer flow model are shown. Convergence is verified of the
maximum water level ascent and descent when the grid sizes are set at L/5, L/10, L/20, and L/40.
The slope incline is fixed at an angle of 6° and roughness coefficient n for the sediment layer at
0.4m-1/3·s.
The maximum water level changes at target sites offshore are shown in Table 4.4.2-4. The
maximum water level changes at target sites along the coastline are shown in Table 4.4.2-5.
Because of the strong directivity that emerged in the solutions using the two-layer flow model,
the rise is dominant for target sites offshore and the fall for target sites along the coastline.
Accordingly, when convergence is verified for the rise at target sites offshore and the fall at target
sites along the coastline, cases where Δx=L/10 show a large difference from cases where Δx=L/40,
and cases where Δx=L/20 showed a difference of ±5% or less than cases where Δx=L/40.
From the above, this calculation example resulted in the maximum water level change
converging for the most part in cases where the size of the landslide area is set at 1/20 in theconfiguration of grid sizes for the two-layer flow model.
Next, the results for the KLS model are shown. Similar to the case of the two-layer flow
model, convergence is verified of the maximum water level ascent and descent when the grid
sizes are set at L/5, L/10, L/20, and L/40. The slope incline is fixed at an angle of 6°, and the
propagation velocity U and duration T at 40m/s and 120s, respectively. The maximum water level
Appendix 4- 88

changes at target sites offshore are shown in Table 4.4.2-6. The maximum water level changes attarget sites along the coastline are shown in Table 4.4.2-7. Cases where Δx=L/20 showed adifference of ±5% or less in comparison to cases where Δx=L/40.
From the above, this calculation example resulted in the maximum water level change
converging for the most part in cases where the size of the landslide area was set at 1/20 in theconfiguration of grid sizes for the KLS model.
Table 4.4.2-4 Maximum water level ascent and descent (Two-layer flow model, offshore)
Water level (m)Relative error for Δx=15m
Grid sizes
Maximum
Maximum
Maximum
MaximumΔx (m)
water level
water level
water level
water levelascentdescent
ascentdescent
15 (=L/40)
0.05219-0.00679－－
30 (=L/20)
0.05453-0.00748
+4.5%
10.2%
60 (=L/10)
0.04963-0.00779
-4.9%
14.7%
120 (=L/5)
0.03675-0.02206-29.6%
224.9%
Table 4.4.2-5 Maximum water level ascent and descent (Two-layer flow model, coast)
Grid sizes
Δx (m)
15 (=L/40)
30 (=L/20)
60 (=L/10)
120 (=L/5)

Water level (m)Maximum
Maximumwater level
water levelascentdescent
0.00703-0.04920
0.00916-0.04801
0.01685-0.04158
0.02347-0.02750

Appendix 4- 89

Relative error for Δx=15m
Maximum
Maximumwater level
water levelascentdescent－－+30.3%-2.4%+139.7%-15.5%+233.9%-44.1%

Table 4.4.2-6 Maximum water level ascent and descent (KLS model, offshore)
Grid sizes
Δx (m)
15 (=L/40)
30 (=L/20)
60 (=L/10)
120 (=L/5)

Water level (m)Maximum
Maximumwater level
water levelascentdescent
0.05057
0.06758
0.04960.07097
0.05327
0.06701
0.06338
0.05289

Relative error for Δx=15m
Maximum
Maximumwater level
water levelascentdescent
－
－
-1.9%
+5.0%
+5.3%
-0.8%
+25.3%-21.7%

Table 4.4.2-7 Maximum water level ascent and descent (KLS model, coast)
Grid sizes
Δx (m)
15 (=L/40)
30 (=L/20)
60 (=L/10)
120 (=L/5)

Water level (m)Maximum
Maximumwater level
water levelascentdescent
0.0176-0.03334
0.01758-0.03372
0.01797-0.03880.01968-0.03807

Relative error for Δx=15m
Maximum
Maximumwater level
water levelascentdescent
－
－
-0.1%
1.1%
2.1%
16.4%
11.8%
14.2%

4.4.2.3. Examination of tsunami originating in slope failures and flank collapses(1) Calculation conditions
1) Topographical conditions
Figure 4.4.2-2 shows a topography for a slope failure and flank collapse. The topography
is configured so that the inclination of slope θ connects to the flat sea bottom having water
depth Hb. On this inclination, the illustrated landslide body has been arranged so that the edge
touches the water surface in its initial state. For the final depositional landform, the KLS modelyielded a distribution that moved in a horizontal direction only in a distance equivalent tolength L of the landslide body from the initial position of the landslide body (zone of depletion).
These configurations have been compiled and given in Table 4.4.2-8.

Appendix 4- 90

Figure 4.4.2-2 Model for slope failure and flank collapse
Table 4.4.2-8 Parameter (slope failure and flank collapse)
Parametervalue

Δh (m)Hb (m)

4080θ (degree)

20,30,40(two-layer flow model),30(KLS model)κ (= lF/lB)
L (m)
W (m)
γ (= ρs/ρwater )
b

1.0
400
400
1.94(=2.0/1.03)
0.5L2) Other conditions
The grid size is based on landslide length L, and was set at L/80, L/40, L/20, L/10 and L/5(=5, 10, 20, 40 and 80m). The appropriate grid size is examined by comparing solutions
obtained using different grid sizes. Tables 4.4.2-9 and 4.4.2-10 show the other calculation
conditions.

Appendix 4- 91

Table 4.4.2-9 Calculation conditions (Slope failure and flank collapse)
Parameter

Value

Grid sizes (m)5,10,20,40,80

Manning’s roughness coefficient between
water and bottom (m-1/3s)

0.03

Kinematic viscosity for water (m2/s)

10.0

Calculation method

Tanaka(1985)’s
methodTable 4.4.2-10 Calculation conditions for each model(Slope failure and flank collapse)
Model

Two-layer
flow model

KLS
model

Parameter

SymbolValue

Computation time interval
Manning’s roughness coefficient forlower layer (soil layer)
Kinematic viscosity for lower layer (soillayer)
resistance coefficient
coefficient for interface resistance force
Computation time interval
Horizontal slide velocity
Rise timeΔt (s)

0.025

n (m-1/3s)

0.4

ν(m2/s)0.01

CD ( - )finter ( - )Δt (s)
U (m/s)
T (s)

0
0
0.1
40
120

(2) Results
The appropriate grid size is examined based upon the results of calculations performed using
the conditions indicated in the previous section.
First, the results of the two-layer flow model are shown. convergence is verified of the
maximum water level ascent and descent when the grid sizes are set at L/5, L/10, L/20, L/40, andL/80.
The water level time history and maximum water level changes at position x=800m havebeen examined. Table 4.4.2-11 shows the maximum water level change in a case where the slope
incline is 20°. Table 4.4.2-12 shows the change in case where the slope incline is 30°, and Table
4.4.2-13 for the case where the slope incline is 40°.
A case study of these results showed that, when the grid size was set between 1/40 and 1/20(=10~20m) for size L of the landslide area, the difference in the maximum water level change
was, for the most part, ±10% or less in comparison to a case where the grid size was set at thesmallest Δx=L/80 (=5m).
Next, the results for the KLS model are shown. Similar to the case of the two-layer flow
model, convergence is verified of the maximum water level ascent and descent when grid sizes
Appendix 4- 92

are set at L/5, L/10, L/20, L/40, and L/80.
The water level time history and maximum water level change at position x=800m havebeen examined. Table 4.4.2-14 shows the maximum water level change in a case where the slope
incline is 30°. Because a value for the fall was not able to be obtained, this calculation verified
the values with respect to rise.
The case of these results showed that, when the grid size was set between 1/40 and 1/10(=10~40m) for size L of the landslide area, the difference in the maximum water level change
was, for the most part, ±10% or less in comparison to a case where the grid size was set at thesmallest Δx=L/80 (=5m).
Table 4.4.2-11 Maximum water level ascent and descent(Two-layer flow model, θ=20°, x=800m)
Grid sizes
Δx (m)
5 (=L/80)
10 (=L/40)
20 (=L/20)
40 (=L/10)
80 (=L/5)

Water level (m)Maximum
Maximumwater level water levelascentdescent
2.767
0.607
3.066
0.654
3.143
0.690
2.098
1.030
1.166
0.461

Relative error for Δx=5m
Maximum
Maximumwater level water levelascentdescent
－
－
10.8%
7.9%
13.6%
13.7%
-24.2%
69.7%-57.9%-24.0%

Table 4.4.2-12 Maximum water level ascent and descent(Two-layer flow model, θ=30°, x=800m)
Grid sizes
Δx (m)
5 (=L/80)
10 (=L/40)
20 (=L/20)
40 (=L/10)
80 (=L/5)

Water level (m)Maximum
Maximumwater level water levelascentdescent
5.196
2.033
5.268
2.139
5.237
1.418
4.012
1.785
1.864
0.696

Appendix 4- 93

Relative error for Δx=5m
Maximum
Maximumwater level water levelascentdescent
－
－
1.4%
5.2%
0.8%
-30.2%-22.8%-12.2%-64.1%-65.8%

Table 4.4.2-13 Maximum water level ascent and descent(Two-layer flow model, θ=40°, x=800m)
Grid sizes
Δx (m)
5 (=L/80)
10 (=L/40)
20 (=L/20)
40 (=L/10)
80 (=L/5)

Water level (m)Maximum
Maximumwater level water levelascentdescent
8.570
2.948
9.210
2.942
7.799
3.480
6.196
3.266
2.308
1.488

Relative error for Δx=5m
Maximum
Maximumwater level water levelascentdescent
－
－
7.5%
-0.2%
-9.0%
18.1%
-27.7%
10.8%-73.1%-49.5%

Table 4.4.2-14 Maximum water level ascent and descent(KLS model, θ=30°, x=800m)
Grid sizes
Δx (m)
5 (=L/80)
10 (=L/40)
20 (=L/20)
40 (=L/10)
80 (=L/5)

Water level (m)Maximum
Maximumwater level water levelascentdescent
0.32
－
0.33
－
0.33
－
0.30
－
0.26
－

Relative error for Δx=15m
Maximum
Maximumwater level water levelascentdescent
－
－
+2.7%
－
+1.4%
－
-8.6%
－
-20.4%－

4.4.2.4. Summary
Case studies were conducted of the appropriate grid size when applying the two-layer flow modeland the KLS model to tsunami originating in submarine landslides as well as slope failures and flankcollapses. The results of the case studies are following:<Submarine landslides>
With both the two-layer flow model and the KLS model, the maximum water level change
converged for the most part in these calculation case studies when the grid size was set at 1/20 ofsize L of the landslide area.

<Slope failures and flank collapses>
With the two-layer flow model, the maximum water level ascent change converged for themost part when the grid size was set at 1/20 of size L of the landslide area. With respect to the
maximum water level descent, there was convergence for the most part in the case where the gridsize was set at 1/40 of size L of the landslide area. However, when compared with the results ofthe examination using tsunami triggered by submarine landslides, the results showed that a
Appendix 4- 94

relatively large difference remained in comparison to a case where the grid size was configured
more minutely.
With the KLS model, the maximum water level ascent converged for the most part when thegrid size was set at 1/10 of size L of the landslide area.
In many cases the length of the tsunami wave following a slope failure or flank collapse wasshorter than that of a tsunami following an earthquake. Attention needs to be given so that thegrid size for the area surrounding the tsunami source region is configured with the precision
sufficient for expressing the spatial tsunami shape of the water level.
4.4.3. Relationship between the calculation tsunami height and the topographical conditions as wellas various parameters
An investigation was conducted for the effects of topographical conditions and various
parameters on calculation tsunami height for the purpose of ascertaining characteristics of numericalmethods. The numerical methods are the two-layer flow model and KLS model. These methods wereapplied to the calculation of submarine landslides in accordance with the virtual topography given in
Appendix Section 4.4.2.2. The following perspectives were adopted for the investigation.
• Relationship of maximum water level change to slope incline• Directivity of maximum water level change• Characteristics of attenuation over distance of the maximum water level change• Relationship between the maximum water level change and the slide velocity• Relationship of maximum water level change to rise time (KLS model)(1) Relationship of maximum water level change to slope incline
Calculations were performed in which slope incline was varied under the following
conditions, and the relationship between slope incline and maximum water level was analyzed.
• Slope incline θ = 3, 6, 12°• Two-layer flow model: Sediment layer roughness coefficient n=0.4m-1/3s• KLS model: U = 40m/s, T = 120s
The other conditions are the same as those for the calculations in Appendix Section 4.4.2.2.
The target sites were x = -2,400m offshore and x = 2,400m along the shore (see Figure 4.4.21).
The relationship between slope incline and maximum water level is shown in Figure 4.4.31.
• With the two-layer flow model, as the slope incline becomes steeper, the intensity of thetsunami becomes greater.
Appendix 4- 95

• With the KLS model, increase in slope incline does not necessarily contribute to an increasein tsunami intensity. Because of this, it has been suggested that attention needs to be givenso that the propagation velocity may be configured in accordance with the slope incline andMaximum water level ascent(m)

Maximum water level ascent(m)
Maximum water level descent(m)

Descent side

Maximum water level descent(m)

Ascent sideother settings aligned in keeping with the parameters.

Figure 4.4.3-1 Slope gradient and maximum water level variations(2) Directivity of maximum water level change
The relationship between tsunami propagation distance and maximum water level change
has been examined for calculations performed under the following conditions, and thecharacteristics related to directivity of each model verified.
• Slope incline θ = 6°
• Two-layer flow model: Sediment layer roughness coefficient n=0.4m-1/3s• KLS model: U = 40m/s, T = 120s
The other conditions are the same as those for the calculations in Appendix Section 4.4.2.2.
The target sites were arranged at 5° intervals on a circle having a radius of 2,400m with its
center at the initial apex of the landslide body (see Figure 4.4.2-1).
Figure 4.4.3-2 shows the relationship between tsunami propagation direction and maximum
water level change. The orientation parallel to the shore is γ=0°, the orientation heading
perpendicular to the shore is γ=90°, and the orientation heading in the opposite direction out to
sea is γ= -90°. The directivity of the maximum water level ascent in the direction out to sea wasverified by both methods. With respect to the maximum water level descent, the two-layer flow
model was in the direction of the shore, and directivity in the direction out to sea was verified forAppendix 4- 96

the KLS model. In particular, directivity verified with the two-layer flow model was more
pronounced than that verified with the KLS model.

Figure 4.4.3-2 Directivity for maximum water level(Two-layer flow model, KLS model)(3) Characteristics of attenuation over distance for maximum water level change
The relationship between tsunami propagation distance and maximum water level change
has been examined for calculations performed under the following conditions, and thecharacteristics verified as pertains to attenuation over distance for each model.
• Slope incline θ = 6°
• Two-layer flow model: Sediment layer roughness coefficient n=0.4m-1/3s• KLS model: U = 40m/s, T = 120s
The other conditions are the same as those for the calculations in Appendix Section 4.4.2.2.
The target sites are points along the linear y=0 (see Figure 4.4.2-1).
Figure 4.4.3-3 shows the maximum water level ascent at the target sites. The axis of
abscissas is x, and the origin is the point of maximum topographic prominence. The absolutevalue of coordinate x is regarded as the propagation distance.
In order to quantitatively express the characteristics of attenuation over distance, therelationship between propagation distance |x| and maximum water level ascent y was regressedin equation y = a ×|x|b. The results are as follows.
• In the case where the coefficient of the regression equation was determined for the sectionout to sea -3,000 < x < -1,500:
Appendix 4- 97

- Two-layer flow

: a = 2.13, b = -0.494- KLS: a = 3.21, b = -0.514• In the case where the coefficient of the regression equation was determined for the section
along the shore 1,500 < x < 3,000:- Two-layer flow

: a = 0.10, b = -0.336- KLS: a = 1.98, b = -0.512

In the case of the point tsunami source, theoretically, the water level is inversely proportional
to the square root of the distance. The regression value of coefficient b is on the order of -1/2 withthe exception of along the shore for the two-layer flow model where amplitude is particularly
small. It was verified that, along the linear y=0, the numerical solution provided by both models
was in accordance for the most part with the theoretical attenuation characteristics of the point
tsunami source.

Figure 4.4.3-3 Distribution of maximum water level ascent (Two-layer flow model, KLS model, y=0)
(4) Relationship between maximum water level change and slide velocity
The relationship between slide velocity and maximum water level has been examined forthe two-layer flow model, and the relationship between propagation velocity and maximum waterlevel for the KLS model. The calculations were performed using the following conditions.
• Slope incline θ = 6°
• Two-layer flow: n=0.2, 0.3, 0.4m-1/3s• KLS: U = 10, 20, 40m/s, T = 120s
The other conditions are the same as those for the calculations in Appendix Section 4.4.2.2.
The target sites were x= -2,400m offshore and x=2,400m along the shore (see Figure 4.4.21).
The slide velocity in the two-layer flow model is the mean velocity defined as L/S where S
is the time required for the point of maximum thickness to move distance L (= 600m) in eachtime series.
Figure 4.4.3-4 shows the relationship between slide velocity and maximum water level
Appendix 4- 98

change. From this examination, it was found that, for both the two-layer flow model and KLS
model, the greater U is, the greater the tsunami intensity becomes. However, the water level inthe KLS model had a greater sensitivity to velocity U. Also, particularly along the shore where itis anticipated a power station will be located, a tendency was observed where the KLS model
assessed the scale of the rise greater, and the two-layer flow model assessed the scale of the fall
to be greater.

Figure 4.4.3-4 Horizontal slide velocity and maximum water level variations(5) Relationship of maximum water level change to rise time (KLS model)
Calculations were performed where rise time T was varied for the KLS model, and therelationship between duration and maximum water level was examined. The calculation
conditions were as given below.
• Slope incline θ = 6°
• KLS: U = 40m/s, T = 120, 240, 480s
The other conditions are the same as those for the calculations in Appendix Section 4.4.2.2.
The target sites were x= -2,400m offshore and x=2,400m along the shore (see Figure 4.4.21).
Figure 4.4.3-5 shows the relationship between duration and maximum water level.
From this examination, it was able to be verified that the shorter the duration, the greater thetsunami intensity becomes with the KLS model.

Appendix 4- 99

Figure 4.4.3-5 Rise time and maximum water level variations (KLS model)
4.4.4. Case studies of historical tsunami caused by factors other than fault motion
The majority of the factors causing tsunami are due to the vertical displacement occurring in theseafloor following fault motion. However, although relatively few in number*, there are also tsunamisthat occur due to factors other than fault motion, such as submarine landslides, slope failures andvolcanic phenomena (flank collapse, caldera collapse, etc.), some of which have caused enormous
damage. This section examines, according to causal factor, notable examples of tsunami that haveoccurred due to factors other than fault motion.
* According to Imamura (1998), tsunami caused by factors other than fault motion account for lessthan 10% of all tsunami.

Appendix 4- 100

4.4.4.1. Tsunami caused by volcanic phenomena (flank collapse)

Name

Ariake Sea Tsunami (torment at Shimabara
and strife at Higo)May 21, 1792
Date

(1st day of 4th month in 4th year of the
Kansei era)

• A volcanic earthquake, which occurred on the night of May 21, 1792 (first day of the 4th month in 4th yearof the Kansei era), caused a large flank collapse at Mt. Tengu, which is a peak of Mt. Mayuyama locatedapproximately 4 km to the east of Mt. Unzen-Fugen, and the flow of debris turned into a flow of earth andstone that plunged into Ariake Sea, triggering a tsunami.
Summary• The large tsunami, which descended on the coastal area of Kumamoto Prefecture (Higo Province) on theother side as well as the coastal area of the Ariake Sea over the entire Shimabara region, is known as thegreatest volcanic disaster in Japan in recorded history with the tsunami reaching heights exceeding 30 to 50
meters at Shimabara and between 15 and 20 meters in Kumamoto City, and a total of 15,000 people either
missing or dead.
Aida, I. (1975) Numerical Experiments of the Tsunami Associated with the Collapse of Mt. Mayuyama in
1792, Zisin (Journal of the Seismological Society of Japan. 2nd ser.), Vol.28, pp.449-460 (in Japanese),https://www.jstage.jst.go.jp/article/zisin1948/28/4/28_4_449/_pdf
Sasahara, N. (2004) Numerical Simulation of the Tsunami caused by the sector Collapse of Mt. Mayuyama,
Shimabara Peninsula, Kyushu in 1792, REPORT OF HYDROGRAPHIC AND OCEANOGRAPHICRESEARCHES No.40 March, pp. 63-72.
http://www1.kaiho.mlit.go.jp/GIJUTSUKOKUSAI/KENKYU/report/rhr40/rhr40-02.pdf
Togashi, H., Y. Hirayama, U. Taniguchi, and S. Matsumoto (1992) Hydraulic experiments of Ariake Sea

Previous
case studies,etc.

tsunami in 1792, Proceedings of Coastal Engineering, JSCE, Vol.39, pp. 221-225 (in Japanese),https://www.jstage.jst.go.jp/article/proce1989/39/0/39_0_221/_article/-char/ja/.
Tsuji, Y. and T. Hino (1993) Damage and Inundation Height of the 1792 Shimabara Landslide Tsunami along
the Coast of Kumamoto Prefecture, Bulletin of the Earthquake Research Institute, University of Tokyo,
Vol.68(2), pp.91-176,
https://repository.dl.itc.utokyo.ac.jp/?action=repository_action_common_download&item_id=32721&item_no=1&attribute_id=19&file_no=1
Tsuji, Y. and Y. Murakami (1997) Run up height of Ariake Sea tsunami on Shimabara peninsula generated bycollapse of Mt. Mayuyama in 1792, Proceedings of Historical Earthquake Studies, JSCE, Vol. 13,
pp.135-173 (in Japanese).

Appendix 4- 101

August 29, 1741
Name

Oshima-Oshima Tsunami

Date

th

(19 day of 7th month in 1st year of the
Kanpo era)

• The Oshima-Oshima tsunami occurred in the sea adjacent to Oshima-Oshima early in the morning of August29, 1741 (19th day of 7th month in 1st year of the Kanpo era). The tsunami height has been estimated tohave been between 3 and 15 meters along the coastline of the Oshima Peninsula and between 4 and 7 meters
along the Tsugaru Peninsula. Estimates have also put the tsunami height between 2 and 5 meters at Sado, 4
meters along the Noto Peninsula, 1 meter at Obama in Fukui Prefecture, 2 meters at Gotsu in Shimane
Summary

Prefecture, and between 3 and 4 meters along the eastern coastline of South Korea.
• This tsunami is said to have resulted in the deaths of 1,467 people (over 2,000 when Ainu and people living
on Honshu are included).
• There are various theories about the cause of the tsunami. It has been pointed out that, at the time, no major
earthquakes had been felt and there is the possibility that the tsunami was triggered by an avalanche ofdebris resulting from a flank collapse following an eruption that began in the western mountains of OshimaOshima around August 18, 1741.
Aida, I. (1984) An Estimation of Tsunamis Generated by Volcanic Eruptions - The 1741 Eruption of OshimaOhshima, Hokkaido., Bulletin of the Earthquake Research Institute, University of Tokyo, Vol.59(4),pp.519-531 (in Japanese),
http://tsunami-dl.jp/document/133
Hatori, T. (1984) Reexamination of Wave Behavior of the Hokkaido-Oshima (the Japan Sea) Tsunami in
1741 : Their Comparison with the 1983 Nihonkai-Chubu Tsunami., Bulletin of the Earthquake ResearchInstitute, University of Tokyo, Vol.59(1), pp.115-125 (in Japanese with English abstract),
https://www.researchgate.net/publication/29773100_beihaidaodudaochongjinbo1741niannojudongnoz
aijiantao_1983nianribenhaizhongbudezhenjinbotonobijiao
Imamura, F. and T. Matsumoto (1998) Field Survey of the 1741 Oshima-Ohshima Volcanic Tsunami, Tsunami

Previous
case studies,etc.

engineering Technical Report, Tohoku University , Vol.15, pp.85-105 (in Japanese).
Katsui, Y., I. Yokoyama, S. Ehara, H. Yamashita, K. Niida, and M. Yamamoto (1977) Oshima-Ohshima.
Report of the Volcanoes in Hokkaido, part 6 Committee for Prevention of the Natural Disasters of
Hokkaido, Sapporo, 82 pp. (in Japanese).
Japan Meteorological Agency (2013) National Catalogue of The Active Volcanoes in Japan (The fourth
edition),http://www.data.jma.go.jp/svd/vois/data/tokyo/STOCK/souran_eng/menu.htm
Satake, K. and Y. Kato (2001) The 1741 Oshima-Oshima Eruption: Extent and Volume of Submarine Debris
Avalanche, Geophysical Research Letters, Vol. 28, No.3, pp.427-430.
Satake, K. and Y. Kato (2002) Collapse of the Oshima-Ohshima Island triggered the 1741 Kampo tsunami,
Kaiyo Monthly, Extra ed.,28, pp.150-160. (In Japanese).
Tsuji, Y., W. S. Beak, K.S. Chu, and H. S. An (1984) Earthquake-induced tsunamis attacked on the eastern
coast of Korea, Kaiyo-kagaku Monthly, 16, pp.527-537. (In Japanese).

Appendix 4- 102

July 31, 1640
Name

Hokkaido-Komagatake Tsunami

Date

th

(13 day of 6th month in 17th year of the
Kan’ei era)

• In the afternoon of July 31, 1640 (13th day of 6th month in 17th year of the Kan’ei era), part of the crest ofa mountain collapsed following a large eruption of the Hokkaido-Komagatake Volcano. An avalanche ofdebris rushed into Onuma Lake and Uchiura Bay, causing a tsunami that descended upon Usu Zenkoji
Summary

Temple on the opposite side and drowned some 700 people.
• Historical descriptions, tsunami deposits, numerical simulations and various other sources of knowledge
have been taken into account in estimating the height of the tsunami, which has been put at between 6 and8 meters along the coastline of Uchiura Bay extending from the west to the north of Komagatake, between
8 and 11 meters from Usu to Muroran, and between 6 and 8 meters from Shiraoi to Tomakomai to the east.
Hatori, T. (1984) Reexamination of Wave Behavior of the Hokkaido-Oshima (the Japan Sea) Tsunami in
1741 : Their Comparison with the 1983 Nihonkai-Chubu Tsunami., Bulletin of the Earthquake ResearchInstitute, University of Tokyo, Vol.59(1), pp.115-125 (in Japanese).
https://www.researchgate.net/publication/29773100_beihaidaodudaochongjinbo1741niannojudongnoz
aijiantao_1983nianribenhaizhongbudezhenjinbotonobijiao
Hokkaido Disaster Management Council (1975) Komagatake – Geological Map, Historical Activity, Volcanic
Activity, and Disaster Prevention, Report of the volcanoes in Hokkaido, part 4. Committee forPrevention of the Natural Disaster of Hokkaido, 194p (in Japanese).
Nishimura, Y. and K. Satake (1993) Numerical computations of tsunamis from the past and future eruptions

Previous
casestudies,etc.

of Komagatake Volcano, Hokkaido, Japan., Proceedings of the IUGG/IOC International Tsunami
Symposium, pp.573-583.
Nishimura, Y. and N. Miyaji (1998) On Height Distribution of Tsunami Caused by the 1640 Eruption of
Hokkaido-Komagatake, Northern Japan., Kazan, Bulletin of the Volcanological Society of Japan,
Vol.43, pp.239-242 (in Japanese),https://www.jstage.jst.go.jp/article/kazan/43/4/43_KJ00001052578/_pdf/-char/ja
Tsuji, Y. (1989) Tsunami from the Eruption of Hokkaido Komagatake on July 31, 1640, The SeismologicalSociety of Japan, 1989 Meeting, Proceedings (1) 261p (in Japanese).
Yohimoto, M., Hurukawa, R., Nanayama, H., Nishimura, Y., Nishina, K., Uchida, Y., Takarada, S., Takahashi,R., Kinoshita, H(2003): Subaqueous distribution and volume estimation of the debris-avalanche deposit
from the 1640 eruption of Hokkaido-Komagatake volcano, southwest Hokkaido, Japan, The Journal of
the Geological Society of Japan, Vol.109,No.10,

pp.595-606 (in Japanese),https://ci.nii.ac.jp/els/contents110003009762.pdf?id=ART0003416282

Appendix 4- 103

4.4.4.2. Tsunami caused by volcanic phenomena (caldera collapse)
Tsunami following eruption of Krakatoa
Name

VolcanoDate

August 27, 1883

(Sunda Strait, Indonesia)• Following a major eruption of Krakatoa Volcano which occurred at 9:58 local time on August 27, 1883,
two-thirds of the island disappeared and a large tsunami occurred in the Sunda Strait that flooded thesurrounding islands. The results of investigations of the traces of this tsunami have found that the
maximum run-up height reached over 30 meters and over 36,000 people died, making it the largest tsunami
disaster in the Indian Ocean until the earthquake off of Sumatra Island in 2004.
Summary• The mechanism, which generated this tsunami, is not clearly understood. If it is assumed that the cause wasa caldera collapse, then the tsunami may be explained by records of tidal observations that, among otherthings, show a predominance of short-period waves inside the Sunda Strait and a predominance of longperiod waves outside the strait.
• Also, based on the results of numerical simulations, it has been pointed out that a tsunami source modelentailing a phreatic explosion underwater is able to explain the results of actual measurements of thetsunami.
Aida, I (1995) The 1883 Krakatau eruption tsunami, Document Editing Society of Diet (Editorial supervisor:
Rikitake, T.), pp.198-199.
Kawamata, S., F. Imamura, and N. Shuto (1992) Numerical simulation of the 1883 Krakatau tsunami,
Proceedings of Coastal Engineering, JSCE, Vol.39, pp.226-230 (in Japanese),

Previous
casestudies, etc.

https://www.jstage.jst.go.jp/article/proce1989/39/0/39_0_226/_pdf
Nomanbhoy, N. and K. Satake (1995) Generation mechanism of tsunami from the 1983 Krakatau eruption,
Geophysical Research Letters, Vol.22, No.4, pp.509-512.
Simkin, T. and R.S. Fiske (1983) Krakatau 1883, The volcanic eruption and its effects, Smithsonian
Institution Press, 464p.
Winchester, S. (2005) Krakatoa: THE DAY THE WORLD EXPLODED: AUGUST 27, 1883, Harper
Perennial; 1st Harper Perennial Ed. Publ. 2005 edition, 416p.

Appendix 4- 104

4.4.4.3. Tsunami caused by submarine landslide
August 24, 1771
Name

Meiwa Yaeyama Earthquake Tsunami

Date(10th day of 3rd month in 8th year of the
Meiwa era)

• Following an earthquake that occurred around 8 AM on April 24, 1771 (10th day of 3rd month in 8th yearof the Meiwa era), a tsunami occurred that resulted in approximately 12,000 dead or missing on the Miyako
Islands and Yaeyama Islands as well as more than 2,000 homes swept away. Based on the results ofinvestigations of the height of traces of the tsunami, it has been found that the run-up height of the tsunami
Summary

reached approximately 30 meters in the southern part of Ishigaki Island and approximately 18 meters in thesouthern part of Miyako Island.
• Based on the results of numerical simulations, it is difficult to explain the run-up height records of tsunami
only from fault displacement on the basis of the earthquake magnitude. Investigations of the sea bottom
topography in the seas around the Yaeyama Islands have confirmed traces of submarine landslides, and it
has been pointed out that it is highly possible the tsunami was caused by a submarine landslide.
Goto, K. and A. Shimabukuro (2012) The 1771 Meiwa tsunami revealing by multidisciplinary researches,
Kagaku, 82, pp.208-214 (in Japanese).
Hatori, T(1987) Tsunami magnitudes and source areas along the Ryukyu islands, Zisin (Journal of the
Seismological Society of Japan. 2nd ser.), Vol.41, pp. 541-547, (in Japanese),https://www.jstage.jst.go.jp/article/zisin1948/41/4/41_4_541/_article
Hiraishi, T., H. Shibaki, and N. Hara (2001) Numerical Simulation of Meiwa-Yaeyama Earthquake Tsunamiin Landslide Model with Circular Rupture, Proceedings of Coastal Engineering, JSCE, Vol.48, pp.351-

Previous
casestudies,etc.

355 (in Japanese),
http://library.jsce.or.jp/jsce/open/00008/2001/48-0351.pdf
Kawana, T., N. Date, T. Nakata, Y. Masaki, N. Simabukuro, R. Hagino, N. Nakasone, and N. Oohashi (2000)
Run up height and movement of reef boulders in Ishigaki island caused by the 1771 Meiwa tsunami,
Proceedings of Historical Earthquake Studies, JSCE, Vol. 17, pp.38-41 (in Japanese).
Matsumoto, T., Kimura, M. (1993) Detailed bathymetric survey in the sea region of the estimated source areaof 1771 Yaeyama earthquake tsunami and consideration of the mechanism of its occurrence, Zisin(Journal of the Seismological Society of Japan. 2nd ser.), Vol.45, pp. 417-426 (in Japanese),https://www.jstage.jst.go.jp/article/zisin1948/45/4/45_4_417/_article/-char/ja/
Nakata, T. and T. Kawana (1986) Seismic tsunami in 1771, Proceedings of Historical Earthquake Studies,
JSCE, Vol. 2, pp.141-147 (in Japanese).

Appendix 4- 105

4.4.4.4. Tsunami caused by flank (slope) collapse
Lituya Bay Tsunami

Name(Alaska, United States)

Date

July 10, 1958

• Following the MW 8.3 earthquake on July 10, 1958, a massive slope failure occurred in the interior of
Lituya Bay along the southern coast of Alaska, and a large quantity of earth, sand and lumps of ice plunged
into the sea, causing a massive tsunami.
• Lituya Bay is a long, narrow and steep fjord that is approximately 11.3 km long and approximately 3.2 km
Summary

wide at the widest point, and fronts the Pacific Ocean. The tsunami, from which there was no place toescape, ran up the slope on the opposite coast and reached an elevation of 524 meters, which is the highest
observation ever recorded. However, as the run-up height of the tsunami approach the bay opening, it
suddenly decreased, and no traces of any impact outside the bay have been observed.
• At Lituya Bay, six flank collapses have been recorded due to similar slope failures.
Aida, I. (1982) Tsunami caused by a sector collapse, Monthly marine sciences, Vol.9, No.2, pp.31-38 (inJapanese).

Previous
casestudies,etc.

Aida, I. (1995) The 1958 Lituya Bay tsunami in Alaska, Document Editing Society of Diet (Editorial
supervisor: Rikitake, T.), pp.202-203 (in Japanese).
Fritz, H.M., F. Mohammed, and J. Yoo (2009): Lituya Bay Landslide Impact Generated Mega-Tsunami 50th
Anniversary, Pure and Applied Geophysics, Feb. 2009, 166, pp.153-175.
Unoki, S. and M. Kubota (1996) Science of Ocean Waves and Currents, Tokai University Press, 356p (inJapanese).

Appendix 4- 106

4.4.4.5. Tsunami caused by other factors

Name

Papua New Guinea Earthquake Tsunami(Sissano coast, West Sepik Province)

Date

July 17, 1998

• At around 18:49 local time on July 17, 1998, a M7.1 earthquake occurred causing a tsunami that resulted
in more than 2,000 deaths along the Sissano coast. The maximum height of the tsunami was over 10
meters, and there was damage over an area extending along 30 kilometers of coastline.
• In comparison to the earthquake magnitude, the intensity of the tsunami was greater. While it has been
pointed out that events other than fault displacement such as landslides triggered by the earthquake wereSummaryfactors causing the tsunami, detailed investigations of the sea bottom topography found distinct
geographical features suggesting that tsunami are more prone to be concentrated along the Sissano coast
than other areas.
• Calculations have been performed using multiple models of the tsunami occurrence and propagation,
but they have not been able to completely explain the results of actual observations, and a conclusionon the factors causing the tsunami has still not been reached.
Hashi, K., and Imamura, F(2000), Study on the Multi-Tsunami Source in the Case of the 1998 Papua New
Guinea Tsunami, Proceedings of Coastal Engineering, JSCE, Vol.47, pp.346-350 (in Japanese),
http://library.jsce.or.jp/jsce/open/00008/2000/47-0346.pdf
Kawada, K., Takahashi, T., Imamura, H., Matsutomi, H., Hujima, K and Matsuyama, M. (1999),
Proceedings of Coastal Engineering, JSCE, Vol.46, pp.391-395 (in Japanese),https://www.jstage.jst.go.jp/article/proce1989/46/0/46_0_391/_article/-char/ja/

Matsuyama,M.,

Imamura, H., Hash
Previous casestudies, etc.

Matsuyama, M., Imamura, H., Hashi, K., Matsumoto and T., Tsuji (1999), Proceedings of Coastal
Engineering, JSCE, Vol.46, pp. 386-390 (in Japanese),https://www.jstage.jst.go.jp/article/proce1989/46/0/46_0_386/_article/-char/ja/
Matsuyama, M., Satake, K. and Matsumoto, T(1999), Proceedings of Coastal Engineering, JSCE, Vol.48,
pp. 366-370 (in Japanese),https://www.jstage.jst.go.jp/article/proce1989/48/0/48_0_366/_article/-char/ja/
Tappin, D. R., T. Matsumoto, P. Watts, K. Satake, G. M. McMurty, M. Matsuyama, Y. Lafoy, Y. Tsuji, T.
Kanamatsu, W. Lus, Y. Iwabuchi, H. Yeh, Y. Matsumoto, M. Nakamura, M. Mahoi, P. Hill, K. Crook,
L. Anton, and J. P. Walsh (1999): Offshore surveys identify sediment slump as likely cause ofdevastating Papua New Guinea Tsunami 1998, EOS, American Geophysical Union, pp.329-340.

Appendix 4- 107

Name

Kocaeli Earthquake Tsunami(Coast of Izmit Bay, Turkey)

Date

August 17, 1999

• At around 3:02 local time on August 17, 1999, a tsunami occurred following the MW 7.4 earthquakewith a seismic center near Izmit City in Turkey. Traces of the tsunami have been confirmed at heightsof 1 to 2.5 meters at the innermost part of Izmit Bay.
Summary• The mechanism of this earthquake was a side slip, which not regarded as often resulting in a tsunami.
However, based on the results of field investigations and numerical simulations, speculation has beenproffered that the earthquake caused fault displacement as well as ground subsidence and coastal
landslides, which occurred in the southern part of Izmit Bay following the earthquake. These
compounded and overlapped, triggering a tsunami.
Altinok, Y., B. Alpar, S. Ersoy, and A. C. Yalciner (1999): Tsunami generation of the Kocaeli earthquake(August 17th 1999) in the Izmit bay; coastal observations, bathymetry and seismic data, Turkish
Journal of Marine Science, Vol.5, No.3, pp.131-148.

Previous casestudies, etc.

Imamura, H., Koshimura, S. and Ahmet C. Yalciner(2000), Proceedings of Coastal Engineering, JSCE,
Vol.47, pp. 331-335 (in Japanese),https://www.jstage.jst.go.jp/article/proce1989/47/0/47_0_331/_pdf
Yalciner A. C., C. E. Synolakis, J. Borrero, Y. Altinok, P. Watts, F. Imamura, U. Kuran, S. Ersoy, U.
Kanoglu and S. Tinti(1999): Tsunami generation in Izumit bay by 1999 Izumit earthquake, Proc. Int.
Conf. on Kocaeli earthquake, ITU, Dec. 2-5, Istanbul, pp.217-221.

Appendix 4- 108

4.5. Basic equations and illustrative calculations for water level fluctuation of sea water intake andoutlet
4.5.1. Basic equation(1) Open channel flow
Basic equations for unsteady flows, which have been utilized for inundation flow, etc., areutilized for the continuity equation as well as the momentum equation for open channel flow.
a. Continuity equation for open channel flow
A Q

0
t
x

b. Momentum equation for open channel flow
 n2 | v | v 1
vv
H
Q
  Q2 0
  gA
 gA 


f
4/3
x
t
x  A 
R
L
g 
2

Of those calculation methods for water channels in Section 6.3.2.1 of the Main Volume, the above basic equations havebeen applied in the following cases.
Main Volume Section 6.3.2.1 (2): Of those cases where all sections are ordinarily open channel flow, method
applying an equation for one-dimensional unsteady flow through an open channel
Main Volume Section 6.3.2.1 (3): Of those cases of both sections with open channel flow and sections withpipeline flow,• Calculation method based on the slot model• Section of open channel flow with a calculation method separating the open channel section and pipeline
section(2) Pipeline flow
In sections where there is pipeline flow (flow in a completely filled state without a free water
surface), the flow cross sectional area fluctuation in the length direction and flow rate fluctuation
are very small, so an expression is used that assumes the first term on the left side of the continuity
equation and the second term on the left side of the momentum equation are each 0 for the
aforementioned open channel flow.
a. Continuity equation for pipeline flow
Q
 0
x

b. Momentum equation for pipeline flow
 n2 | v | v 1
vv
Q  Q2 H0  gA
f
 gA 

4/3
t
x  A 
R
L
g 
x
2


Appendix 4- 109

Of those calculation methods for water channels in Section 6.3.2.1 of the Main Volume, the above basic equations havebeen applied in the following cases.
Main Volume Section 6.3.2.1 (1): Cases where all sections are ordinarily pipeline flow
Main Volume Section 6.3.2.1 (3): Of those cases of both sections with open channel flow and sections with pipelineflow,• Section of pipeline flow with a calculation method separating the open channel section and pipeline
sectionwhere, t: time, Q: flow rate, v: flow velocity, x: coordinate along the water channel, A: flow crosssectional area, H: pressure head + potential head (case of pipeline flow), potential head (case ofopen channel flow), z: water channel bed height, g: acceleration of gravity, n: Manning’s
roughness coefficient, R: hydraulic radius, L: length of water channel flow direction, and f: local
loss coefficient.
4.5.2. Illustrative calculation conditions
An examination is conducted of the water intake facility model shown in Figure 4.5.2-1.

Model A
Eigen period of pipeline flow：189sec(About 3min)+10.0mWater Tank

Open sea

2

Area 800m
Rectangular channel(Height 6m,Width 6m)-10.0m

-11.0mLength of water channnel 400m (Δx=5m)
Manning’s roughness coefficient 0.02(m

-1/3

s)

Model B(Models A with 7m rising in channel bottom height and 3m in channel height)+5.0m
Eigen period of pipeline flow: 268sec(About 4.5min)
Open sea

Water Tank
2

Rectangular channel(Height 3m, Width 6m)-4.0m

Area 800m-3.0m

Length of water channnel 400m (Δx=5 m)
Manning’s roughness coefficient 0.02(mFigure 4.5.2-1 The water intake facility model

Appendix 4- 110

-1/3

s)

The principal calculation conditions are given below.
• The numerical methods are a numerical method that separates the water channel portion into
a section for open channel flow and a section for pipeline flow, and a numerical method forthe water tank portion that is based upon a model taking into account only fluctuations inwater volume inside the tank (see Main Volume Section 6.3.2).
• Data on the perimeter water level in the open sea is the following three types.
[1] Inherent period 30sec., sine wave having a semi-amplitude of 2m[2] Inherent period 20min., sine wave having a semi-amplitude of 2m[3] Simulated tsunami waveform (see Figure 4.5.2-2)
5
水位(m)
Water
Level (m)

4
3
2
1
0
‐1
‐2
‐3
0

20

40

60

80

100

120

140

160

180

200

220

240

時間（分）
Time
(min.)

Figure 4.5.2-2 Simulated Tsunami waveform• Pump water intake volume: 0.0m3/s• Computation time interval: 0.05sec
The cases examined are the four cases indicated in Table 4.5.2-1.
Table 4.5.2-1 List of calculation of water level fluctuation of the sea water intake and outlet
Case

Model

Waveform of open sea

Flow

Case1

Model A

Sine wave（Period 30 sec.）

All sections are pipeline flow

Case2

Model A

Sine wave（Period 20 min.）All sections are pipeline flow

Case3

Model A

Simulated tsunami waveform

All sections are pipeline flow

Case4

Model B

Simulated tsunami waveform

Both sections with open channel
flow and sections pipeline flow

4.5.3. Results of illustrative calculations
Table 4.5.3-1 shows the maximum and minimum water levels based upon the results ofAppendix 4- 111

calculations for the four cases indicated in Table 4.5.2-1. Figure 4.5.3-1 shows a time series graph foreach case. The examination results are consolidated below.
• From the results of Case 1 shown in Figure 4.5.3-1(a), there is almost no change in the waterlevel of the water intake tank. This is because the inherent period (30 seconds) of the open sea
water level tsunami waveform is a shorter period than the eigen period for the facility (3minutes), so the water tank water level did not respond to changes in the water level in the
open sea.
• From the results of Case 2 shown in Figure 4.5.3-1(b), the fluctuation in the water level of thewater intake tank is the same as that for the open sea. This is because the longer the inherent
period becomes of the open sea water level tsunami waveform in comparison to the eigen
period of the facility, change in the water level of the water tank becomes coincides more withthe water level in the open sea.
• From the results of Case 3 shown in Figure 4.5.3-1(c), it is able to be verified that thecomposition of the inherent period of 3 minutes, which is included in the water level for the
open sea (= eigen period for the facility), is amplified in the water tank.
• In the results of Case 4 shown in Figure 4.5.3-1(d), all sections are in a state of open channel
flow due to initial drawback, and the subsequent sudden leading wave forms a bore within thewater channel which then immediately becomes a state of pipeline flow. The water intake tankwater level subsequently reaches its highest height, and, thereafter as well, fluctuation in thewater level in the open sea results in a mix of open channel flow and pipeline flow.
Figure 4.5.3-1 List of the maximum and minimum water levels based upon yhe results of calculations
Case

Model

Waveform of open sea

Water level ofopen sea(m)Water level ofwater tank (m)

max

min

max

min

Case1

Model A

Sine wave（Period 30 sec.）

2.00

-2.00

0.06

-0.06

Case2

Model A

Sine wave（Period 20 min.）

2.00

-2.00

2.05

-2.05

Case3

Model A

Simulated tsunami waveform

4.05

-1.48

6.72

-3.99

Case4

Model B

Simulated tsunami waveform

4.05

-1.48

4.60

-1.94

Appendix 4- 112

Water水位(m)Level (m)3Open
外海 sea
取水槽tank
Water

2
1
0
‐1
‐2
‐3
0

1

2

3

4

5

6

7

8

9

10

時間（分）
Time
(min.)(a) Case1 (Model A, Sine wave (Period 30 sec.) )Water水位(m)Level (m)3

外海 sea
Open
取水槽tank
Water

2
1
0
‐1
‐2
‐3
0

10

20

30

40

50

60

70

80

90

100

110

120

Time
(min.)
時間（分）(b) Case2 (Model A, Sine wave (Period 20 min.) )Water水位(m)Level (m)8Open
外海 sea
取水槽tank
Water

6
4
2
0
‐2
‐4
‐6
0

10

20

30

40

50

60

70

80

90

100

110

120

時間（分）
Time
(min.)

Water水位(m)Level (m)(c) Case3 (Model A, Simulated tsunami waveform)
5
4
3
2
1
0
‐1
‐2
‐3

Open
外海 sea
取水槽tank
Water

0

10

20

30

40

50

60

70

80

90

100

時間（分）
Time
(min.)(d) Case4 (Model B, Simulated tsunami waveform)
Figure 4.5.3-1 A time series graph for each caseAppendix 4- 113

110

120

4.6. Heights of traces of historical tsunami and tide gauge records
4.6.1. Methods for classifying the reliability of historical tsunami trace heights
The confidence of data on the heights of traces of historical tsunami varies in each individual
case depending upon how well defined the traces are and the certainty of information sources. In an
investigation of tsunami height after the 1960 Chile earthquake tsunami, data on the height of thetsunami traces was classified based upon the standards described in levels A, B and C of Table 4.6.11 in accordance with the degree to which the traces were defined and the magnitude of themeasurement error (Chile Tsunami Joint Investigation Team, 1961). Subsequent investigations havealso followed this classification for the most part. Moreover, when an investigation was conductedof the earthquake tsunami off the eastern coast of Hokkaido in 1994, level D in Table 4.6.1-1 wasadded (Shuto and Unohana, 1995).
Based upon a similar approach, Table 4.6.1-2 is presented as a standard for classifying theheights of traces of historical tsunami prior to the 1960 Chilean tsunami, which are described inhistorical material and other sources (Japan Society of Civil Engineers, 2002).
The descriptions given in levels A and B concerning confidence are used in comparisons withtsunami calculations. In cases where there are very few traces of a tsunami, those descriptions inlevel C or below may be the focus.

Appendix 4- 114

Table 4.6.1-1 Classification of confidence levels of run-up height records of tsunami (After 1960
Chilean Tsunami)

Confidence

Judgment criteria

AHigh confidence level.
Clear traces with minor survey errors.

B

Moderate confidence level.
Traces are obscure, but the surrounding conditions and witnesses indicate a reliable
water level. Survey errors are insignificant.

C

Low confidence level.
Traces indicating waves having abnormally landed a sand beach, etc. or traces withsignificant survey errors due to survey points located away from the seashore.

D

Extremely low confidence level.
Obscure traces overlapped by the effect of high water or typhoons etc. or folklore orother ungrounded information.

Table 4.6.1-2 Classification of confidence levels of run-up height records of tsunami (Before 1960
Chilean Tsunami)
Japan Society of Civil Engineers (2002)[Notes on the confidence of ancient document records (Nobuo Shuto)]
Judgment criteria

Confidence

A

B

C

D

High confidence level.
Trace Information is described in ancient texts and local historical documents, etc., aswell as site can be confirmed at present.etc., as well as site can be confirmed at present.
Furthermore, trace height is surveyed and determined in recent years.
Moderate confidence level.
Trace Information is described in ancient texts and local historical documents, etc., aswell as site can be confirmed at present. However, trace height is not re-surveyed inrecent years.
Low confidence level.
Trace Information is described in ancient texts or told from mouth to mouth. However,
the information is only limited to the name of regions and villages. Location of tracecannot be tacked.
Only as reference.
Information speculated from relevant phenomena and descriptions on damage describedin ancient texts.

4.6.2. Relationship between heights of traces of historical tsunami and tide gauge records
Depending upon the frequency response characteristics of tidal wells which are attributable tothe structure of the tidal well, tide gauge records omit short period elements of tsunami (this is known
as a “hydraulic filter”). Satake et al. (1988) show the typical structure of a tidal well in Japan. The tidegauge itself is set inside the tidal well, and the well is connected with the open sea by means of a
Appendix 4- 115

conduit. The conduit functions to remove short period elements that also result from ocean tides.
Accordingly, these conduits also affect tsunami records (Satake, 1991).
After the 1983 Nihonkai-Chubu earthquake, the response characteristics of tidal wells were
investigated, and a method proposed for correcting tide gauge records. For an example of thecorrection of tide gauge records and the response characteristics of tidal wells, see Satake et al. (1988).
Kajiura (1983) investigated the relationship between the peak overall amplitude in the tide gauge
records and the run-up height around tide gauges, which was:
(Run-up height) ≃ (Tide gauge record peak overall amplitude)
If the water level ascent and descent due to tsunami is almost equal, then this shows that the
maximum water level ascent based upon tide gauge records is equivalent to approximately half of the
run-up height on average. In other words, the relationship is:(Run-up height) ≃ (Tide gauge record maximum water level ascent) × 2

4.6.3. Inversion Analysis of Tsunami
References on tsunami inversion can be found in Satake et al. (2013). This case study ispresented of a linear inversion analysis that takes into consideration shallow water deformation
based upon the method presented by Annaka et al. (1999) for the 1944 Tonankai Earthquake.
(1) Analysis method
1) Configuration of tsunami source model
The tsunami source model, which would serve as the foundation, was configured asindicated below.
• Subduction zone surface: The subduction zone depth (10~30 km) was adopted based upon
Kaneda and Baba (2006)• Slip direction: Configured with reference to Sagiya (1999) and Nishimura et al. (1999)
2) Configuration of calculation grid model
For verification of the reproducibility of tsunami observation records, the results were
utilized of calculations performed using a land run-up model with a grid size of 50m along thecoastline (Pacific coastline from Chiba Prefecture to Kyushu was partitioned into four regions).
For the inversion analysis, calculation of Green’s function and a series of tsunami iterations
were necessary, so the simulating time was shortened by using a rough grid model with gridsof 400m along the coastline (50-meter grid model only at tidal observation record points).
3) Configuration of evaluation function
Evaluation function J, which was used for inversion, is given below.

Appendix 4- 116

J  C1 









 C3 

n 2 n3
 B iO  B iC
n 3 i 1

2

n 2 l   C    Z   Z n 2 n1
 log 10 A NLO i  log 10 k i  A NLC i
n1 i 1n0

2

l 1 i 1

O
NL

i ,l

C
NL

i  ts l , l  W   ts 
2

n0

l 1

2

l

2

     m 
2

2

2

i, j

where,

n1: total data number of the height of tsunami traces,n2: total data number of tidal observation records,
n3: total data number of crustal movement,
n0: number of tidal observation records point,n’21: number of data per tidal observation records point ,AONL: height of tsunami traces,
ACNL: the calculation maximum water level (shallow water equation),
ZONL: height of tidal observation records at arbitrary time,
ZCNL: the calculation height at tidal observation records point (shallow water equation),
BO: observed crustal movement data,
BC: the calculation crustal movement data,k: conversion coefficient of calculation result of rough grid model and detailed grid model,
C1: weight for SSR of the height of tsunami traces,
C2: weight for SSR of tidal observation records,
C3: weight for SSR of crustal movements,
ts: the calculation tsunami waveform time shift,
W: weight for the calculation tsunami waveform time shift, andγ: weight for the smoothing constraint.
n si

2mi   mbi , j  nsi  m
j 1

mi: slip amount of i th segment, andmbi,j: the j th slip amount adjacent to the i th segment
The height of tsunami traces, tidal observation records and the amount of crustal
movement were reproduced, and C1 : C2 : C3 , which was weighted for the sum of the squared
residuals of these, were all 1. Also, the inversion was performed using zero for W weighted
for the extent of the calculation tsunami waveform time shift and 

weighted for thesmoothing constraint. Tsunami calculations were performed using grid models based upon amodel having uniform slippage in all tsunami source regions, and the coefficient for each point,
which was used to convert the results of calculations using a rough grid model with 400-meter
grids along the coastline into the results of calculations using a detailed grid model with 50Appendix 4- 117

meter grids along the coastline, was the ratio of the calculation maximum water level for eachpoint marking a trace of the tsunami.
(2) Reproduced data
1) Run-up height of past tsunami
From data for points where traces of the tsunami were identified on the tsunami
calculation grid (50-meter grid), those points which appeared to have originated due to river
run-up or other such circumstances were omitted, and the data for tsunami traces at 64 sites
was adopted.
2) Tidal observation records
The target records are for the following 10 points: Mera, Yokosuka, Ito, Uchiura, Fukue,
Morozaki, Matsusaka, Shimotsu, Muroto and Tosashimizu.
A band pass filter having inherent periods ranging from 5 minutes to 3 hours was applied
to remove short period elements included due to digitalization and tide elements. The tsunami
waveform data intervals were set at 10 seconds.
3) Crustal movement
The values for 12 points based upon Omote (1946) were used as the observed values forcrustal movements.
(3) Inversion results
Figure 4.6.3-1 shows a map of the locations of faults of the 1944 Tonankai earthquake andthe observation locations. Figure 4.6.3-2 shows crustal movement and site locations. Because
setting a configuration for each small fault is difficult due to the relationship of the amount ofobservation data, the fault slippage, which was estimated by inversion, was computed bygrouping together small faults for a total of 18 slippage groups.
Figure 4.6.3-3 shows the fault slippage distribution estimated by inversion. Moreover,Figure 4.6.3-4 shows a comparison of the observation results and calculation results using
detailed 50m grids along the coastline based upon the configured tsunami source model. The
indices K and κ, which were set forth by Aida (1977) based upon the configured tsunami source
model are given below.

K=1.14, κ=1.44 (number of sites: 64)
Although K did not really satisfy the compatibility conditions, κ, which was the indicatorfor variance, satisfied the conditions of 0.95  κ  1.45 (Japan Society of Civil Engineers, 2002).
Also, tidal records and crustal movement were able to reproduce, for the most part, observation
records.

Appendix 4- 118

Yokosuka
UchiuraMorosaki

Ito

Fukue

Mera

Matsusaka

Shimotsu

MurotoTosashimizu

Number of Estimate: 18: Trace spot
: Tide record point (Place name notation)

Figure 4.6.3-1 Locations of faults of the 1944 Tonankai Earthquake and Tsunami observation

Nishiura 0.00
Maisaka -0.10
Omaezaki 0.30
Fukue -0.20

Matsusaka -0.40

Owase -0.20
Kuki -0.40
Atashika -0.30
Tomari -0.20
Shingū -0.30
Katsuura -0.45
Shionomisaki -0.10

Unit : m

Figure 4.6.3-2 Crustal movements of the 1944 Tonankai Earthquake

6
5

C
4

B

Unit : m3
2

A
1

Number of Estimate：18

Average slip less
Average slip or more and less than twice the average slip amountMore than twice the average slip amount

Average slip amount：1.80m
Mw 8.11

Figure 4.6.3-3 Fault slippage distribution estimated by inversion of the 1944 Tonankai Earthquake
Appendix 4- 119

Tsunami height(m)

10

1

0.1

0.4
0.3
0.2
0.1
0.0
-0.1
-0.2
-0.3
-0.4
-0.5

1.5

Water level(m)

0.0
-0.5
-1.0
-1.5
20

40

60

80

100

0.0
-0.5
-1.0
-1.5

120

0

20

40

Ito
Water level(m)Water level(m)

0.0
-0.5
-1.0

Crustal movement
SSR

20

40

60

80

100

0.0
-0.5
-1.0
0

120

20

40

1.5

80

100

120

100

120

100

120

T ime（min.）

1.5

Fukue

1.0

60

Morozaki

1.0
Water level(m)

0.5
0.0
-0.5
-1.0
-1.5

0.5
0.0
-0.5
-1.0
-1.5

0

20

40

60

80

100

120

0

20

40

T ime（min.）

1.5

80

T ime（min.）1.5

Matsusaka

1.0

60

Shimotsu

1.0
Water level(m)

0.5
0.0
-0.5
-1.0
-1.5

0.5
0.0
-0.5
-1.0
-1.5

0

20

40

60

80

100

120

0

20

40

T ime（min.）1.5

Muroto

1.0

60

80

T ime（min.）1.5

Tosashimizu

1.0
Water level(m)

0.5
0.0
-0.5
-1.0
-1.5

Obs

Cal

0.5
0.0
-0.5
-1.0
-1.5

0

20

40

60

80

100

120

0

20

40

T ime（min.）

60

80

100

120

T ime（min.）Figure 4.6.3-4 Reproduction result by inversion of the 1944 Tonankai Earthquake
Appendix 4- 120

0.25

SSR of Tidal observation
Mera
21.25
Yokosuka
9.73
Ito
12.41
Uchiura
31.26
Fukue
2.69
Morozaki
11.15
Matsusaka
8.18
Shimotsu
20.23
120
Muroto70.20
Tosashimizu
8.26
total
195.36

0.5

T ime（min.）Water level(m)100Height of tsunami traces
K
1.142
κ
1.440
SSR
9.31

-1.5
0

Water level(m)80Uchiura

1.0

0.5

-1.5

Water level(m)60

T ime（min.）

1.5

1.0

Omaezaki

0.5

T ime（min.）1.5

Maisaka

Fukue

Nishiura

Yokosuka

1.0

0.5

0

Matsusaka

Owase

Kuki

Atashika

Tomari

Katsuura

1.5

Mera

1.0
Water level(m)Shingū

Obs(Omote,1946)
Cal

Shionomisaki

Crustal movement(m)0.01

Tannowa
Shimotsu
Taiji
MoriuraUragamiShimosato
YukawaKoshinoyu
Katsuura-kou
Katsuura
Tenma
Nachi
Kujinokawa
Ugui
Shingū
Kinomoto
Odomari
Kodomari
IsozakiAtashika
Yuki
Komukai
Nigishima
Hobo
Kajika
Sone
Kata
Furue
Mikisato
NagaraKowaki
MikiuraSagarimatsu
Haida
Kuki
Matsumoto
Osoneura
Mukai
Yanohama
Owase
Tenma
Furusato
MizuchiHikimoto
Nagahama
YaguchiNagashima
NaguraNishikiShimazu
Kamisakiura
Toba
Matsusaka
UtsumiMorosakiNishiura
Fukue
OmaezakiUchiuraShimodaIto
Misaki
Yokosuka
Mera

Obs
Cal

[Appendix 4 References]
Aida, I. (1975): Numerical Experiments of the Tsunami Associated with the Collapse of Mt.
Mayuyama in 1792, Zisin (Journal of the Seismological Society of Japan. 2nd ser.), Vol. 28,
pp. 449-460 (in Japanese).
https://www.jstage.jst.go.jp/article/zisin1948/28/4/28_4_449/_pdf
Aida, I. (1977): Simulations of Large Tsunamis Occurring in the Past off the Coast of the Sanriku
District., Bulletin of the Earthquake Research Institute, University of Tokyo, Vol. 52(1), pp.
71-101 (in Japanese)
https://repository.dl.itc.utokyo.ac.jp/?action=repository_action_common_download&item_id=33218&item_no=1&att
ribute_id=19&file_no=1
Aida, I. (1993): Historical Tsunamis and their Numerical Models which Occurred in the North-WesternPart of Sagami Bay, Journal of Geography, Vol. 102, No. 4, pp. 427-436 (in Japanese).
https://www.jstage.jst.go.jp/article/jgeography1889/102/4/102_4_427/_pdf
Annaka, T., K. Ohta, H. Motegi, I. Yoshida, M. Takao and H. Soraoka (1999): Tsunami Inversion
Based on the Shallow Water Theory, Proceedings of Coastal Engineering, JSCE, Vol. 46, pp.
341-345 (in Japanese).
https://www.jstage.jst.go.jp/article/proce1989/46/0/46_0_341/_pdf/-char/ja
Arikawa, T., F. Yamada and M. Akiyama (2005): Study of Applicability of Tsunami Wave Force inThree-Dimensional Numerical Wave Tank, Proceedings of Coastal Engineering, JSCE, Vol. 52,
pp. 46-50 (in Japanese).
Arimitsu, T., Kazuya Ooe and Koji Kawasaki (2012): Proposal of Evaluation Method of Tsunami
Wave Pressure Using 2D Depth-Integrated Flow Simulation, Journal of Japan Society of Civil
Engineers, Ser. B2 (Coastal Engineering), Vol. 68, No. 2, pp. I-776-I-780 (in Japanese).
Arimitsu,T., T. Deguchi, K. Ooe and K. Kawasaki (2013): Applicability of Evaluation Method of
Tsunami Wave Pressure Using Hydraulic Quantities at Front of Land Structure to Multiple
Structures, Journal of Japan Society of Civil Engineers, Ser. B2 (Coastal Engineering), Vol. 69,
No. 2, pp. I-321-I-325 (in Japanese).
Boussinesq, J. (1872): Théorie des ondes et des remous qui se propagent le long d’un canalrectangulaire horizontal, au communiquant an liquide contenue dans ce canal des vitesses
sensiblement pareilles de la surface au fond, Liouvilles Journal de mathématiques pures etappliquées, Vo. 17, pp. 55-108.
Central Disaster Management Council (2002): The 6th meeting of Tonankai/Nankai Earthquake
Countermeasure Expert Committee (in Japanese).
http://www.bousai.go.jp/kaigirep/chuobou/senmon/tounankai_nankaijishin/6/pdf/siryou1.pdf
Appendix 4- 121

Coastal Development Institute of Technology (2010): Research and Development on CADMASSURF/3D, Report of Study Group on Application of Three-Dimensional Numerical Wave Tank
to Maritime Structures Design, Coastal Technology Library, No. 39 (in Japanese).
Committee for the Field Investigation of the Chilean Tsunami of 1960 (1961): The Chilean tsunami of
May 24, 1960, Earthquake Research Institute, The University of Tokyo, 397p. (in Japanese).
Fujikawa, Y. (1982): Method for Solving of the partial differential equation with the computer, pp.
144-145, SAIENSU-SHA Co., Ltd. (in Japanese).
Goto, C. and Y. Ogawa (1982): Tsunami numerical simulation with leapfrog scheme, School ofEngineering, Tohoku University, 52p. (in Japanese).
Goto, C. and N. Shuto (1983): Numerical simulation of tsunami propagations and run-up, Tsunamis:
Their Science and Engineering, pp. 439-451.
Goto, C. (1984): EQUATIONS OF NONLINEAR DISPERSIVE LONG WAVES FOR A LARGEURSELL NUMBER, Journal of Japan Society of Civil Engineers, Volume 1984, Issue 351, pp.
193-201 (in Japanese).
https://doi.org/10.2208/jscej.1984.351_193
Goto, C., F. Imamura and N. Shuto (1988): Study on Numerical Simulation of the Transoceanic
Propagation of Tsunami Part 1: Governing Equation and Mesh Length, Journal of the
Seismological Society of Japan. 2nd ser., Volume 41, Issue 4, pp.515-526 (in Japanese).
https://doi.org/10.4294/zisin1948.41.4_515
Goto, C. and K. Sato (1993): Development of Tsunami Numerical Simulation System for Sanriku
Coast in Japan, Report of the Port and Harbor Research Institute, Vol. 32, No. 2, pp. 3-44 (inJapanese).
http://www.pari.go.jp/search-pdf/vol032-no02-01.pdf
Goto, H., H. Ikari, T. Matsubara and T. Ito (2011): Numerical Simulation on Tsunami due to Sector
Collapse by Solid-Liquid Two-Phase Flow Model Based on Accurate Particle Method, Journalof Japan Society of Civil Engineers, Ser. B2 (Coastal Engineering), Vol. 67, No. 2, pp. I_196I_200 (in Japanese).
https://doi.org/10.2208/kaigan.67.I_196
Grilli, S. T. and P. Watts (2005): Tsunami Generation by Submarine Mass Failure. I: Modeling,
Experimental Validation and Sensitivity Analyses, Journal of Waterway, Port, Coastal, andOcean Engineering, 131:6(283), 283-297.
Hasegawa, K., T. Suzuki, K. Inagaki and N. Shuto (1987): A STUDY ON THE MESH SIZE AND
TIME INCREMENT IN THE NUMERICAL SIMULATION OF TSUNAMIS, Journal ofJapan Society of Civil Engineers, Volume 1987, Issue 381, pp. 111-120 (in Japanese).
https://doi.org/10.2208/jscej.1987.381_111
Hashi, K. and F. Imamura (2000): Study on the Multi-Tsunami Source in the Case of the 1998 Papua
Appendix 4- 122

New Guinea Tsunami, Proceedings of Coastal Engineering, JSCE, Vol. 47, pp. 346-350 (inJapanese).
http://library.jsce.or.jp/jsce/open/00008/2000/47-0346.pdf
Hiraishi, T., H. Shibaki and N. Hara (2001): Numerical Simulation of Meiwa-Yaeyama Earthquake
Tsunami in Landslide Model with Circular Rupture, Proceedings of Coastal Engineering, JSCE,
Vol. 48, pp. 351-355 (in Japanese).
http://library.jsce.or.jp/jsce/open/00008/2001/48-0351.pdf
Imamura, F. and M. M. A. Imteaz (1995): Long waves in two-layers: Governing equations andnumerical model, Science of Tsunami Hazards, Vol. 13, pp. 3-24.
Imamura, F. (1998): Development of tsunami numerical calculation in 15 years and future, Kaiyo extra(15), pp. 89-98 (in Japanese).
Imamura, F. and H. J. Lee (1998): State-of Arts of Numerical Simulations for Generation and
Propagation of Tsunamis, Bulletin on Coastal Oceanography, Vol. 36, No. 1, pp. 91-101 (inJapanese).
https://projects.repo.nii.ac.jp/?action=repository_uri&item_id=47487&file_id=21&file_no=1
Imamura, F., D. Goto, Y. Shigihara, Y. Kitamura, T. Matsubara, K. Takaoka and K. Ban (2001): Studyon the Tsunami Generation due to Rush of a Landslide into Water, Proceedings of Coastal
Engineering, JSCE, Vol. 48, pp. 321-325 (in Japanese).
http://library.jsce.or.jp/jsce/open/00008/2001/48-0321.pdf
Inagaki, K., M. Koba, H. Tanaka and M. Takao (2001): Study on the Grid Size for V-Shaped Bay andPort in Tsunami Computation, Proceedings of Coastal Engineering, JSCE, Vol. 48, pp. 336340 (in Japanese).
http://library.jsce.or.jp/jsce/open/00008/2001/48-0336.pdf
Ishibashi, K. (1976): Reexamination of a major earthquake expected in the Tokai district - About Gulf
of Suruga major earthquake-, The Seismological Society of Japan, 1976 Meeting, Proceedings(2) pp. 30-34 (in Japanese).
Iwasaki, T. and A. Mano (1979): Two-dimensional numerical simulation of tsunami run-ups in the
Eulerian description, Proceedings of Coastal Engineering, JSCE, Vol. 26, pp. 70-74 (inJapanese).
http://library.jsce.or.jp/jsce/open/00008/1979/26-0070.pdf
Iwase, H., M. Fukasawa and C. Goto (2001): Hydraulic Experiment and Numerical Simulation for
Breaking Wave Transformation of Disintegrated Soliton Waves, Proceedings of Coastal
Engineering, JSCE, Vol. 48, pp. 306-310 (in Japanese).
http://library.jsce.or.jp/jsce/open/00008/2001/48-0306.pdf
Iwase, H., C. Goto, K. Fujima and K. Iida (2002): THE DISPERSION EFFECT ON THE
PROPAGATION OF TSUNAMI IN DEEP SEA REGION, Journal of Japan Society of Civil
Appendix 4- 123

Engineers, Volume 2002, Issue 705, pp. 101-114 (in Japanese).
https://doi.org/10.2208/jscej.2002.705_101
Kajiura, K. (1983): Some statistics related to observed tsunami heights along the coast of Japan,
Tsunamis-Their Science and Engineering, Iida, K. and T. Iwasaki (ed.), pp. 131-145.
Kawamata, K., K. Takaoka, K. Ban, F. Imamura, S. Yamaki and E. Kobayashi (2005): Model oftsunami generation by collapse of volcanic eruption: The 1741 Oshima-Oshima tsunami,
Tsunamis: Case Studies and Recent Developments, pp. 79-96, L. Satake (ed.), Springer.
Kawasaki, K., S. Yamaguchi, M. Hakamata, N. Mizutani and S. Miyajima (2006): Wave Pressure
Acting on Drifting Body after Collision with Bore, Proceedings of Coastal Engineering, JSCE,
Vol. 53, pp. 786-790 (in Japanese).
Kawasaki, K. and M. Hakamata (2007): Development of Three-Dimensional Numerical Model ofMultiphase Flow “DOLPHIN-3D” and Dynamic Analysis of Drifting Bodies under Wave
Actions, Proceedings of Coastal Engineering, JSCE, Vol. 54, pp. 31-35 (in Japanese).
Kawasaki, K., S. Matsuura and T. Sakatani (2013): Validation of Free Surface Analysis Method inThree-Dimensional Computational Fluid Dynamics Tool “OpenFOAM”, Journal of Japan
Society of Civil Engineers, Ser. B3 (Marine Development) Vol. 69, No. 2, pp. I_748-I_753 (inJapanese).
Kaneda, Y. and T. Baba (2006): REGIONAL CHARACTERIZATION OF THE CRUST IN
METROPOLITAN AREAS FOR PREDICTION OF STRONG GROUND MOTION,“Special Project for Earthquake Disaster Mitigation in Urban Areas”, Ministry of Education,
Culture, Sports, Science and Technology (MEXT), Japan, pp. 490-500 (in Japanese).
http://www.eri.u-tokyo.ac.jp/daidai/h17seika-hokokusho/honbun_final/3_3_3_10(pp.490500).pdf
Kihara, N. and M. Matsuyama (2010): On applicability of the hydrostatic 3-D tsunami analysis system
Tsunami to tsunami-induced sediment transport-Simulations of sediment transport around theKirinda port induced by the Indian Ocean tsunami, Central Research Institute of Electric Power
Industry Reports, N09004 (in Japanese).
Kihara, N., N. Fujii and M. Matsuyama (2012): Three-dimensional sediment transport processes ontsunami-induced topography changes in a harbor, Earth Planets Space, Vol. 64, pp. 787-797.
Kotani, M., F. Imamura and N. Shuto (1998): Tsunami Run-Up Simulation and Damage Estimation
by Using GIS, Proceedings of Coastal Engineering, JSCE, Vol. 45, pp. 356-360 (in Japanese).
http://library.jsce.or.jp/jsce/open/00008/1998/45-0356.pdf
Lynett, P. and P. L.-F. Liu (2005): A numerical study of the run-up generated by three-dimensionallandslides, Journal of geophysical research, Vol. 110, C03006.
Madsen, P.A. and O. R. Sørensen (1992): A New Form of the Boussinesq Equation with Improved
Linear Dispersion Characteristics, Part 2, A Slowly-Varying Bathemetry, Coastal Engineering,
Appendix 4- 124

Vol. 18, pp. 183-204.
Maeno, F. and F. Imamura (2007): Numerical investigations of tsunamis generated by pyroclastic
flows from the Kikai caldera, Japan, Geophysical Research Letters, 34:L23303.
Maeno, F. and F. Imamura (2011): Tsunami generation by a rapid entrance of pyroclastic flow into thesea during the 1883 Krakatau eruption, Indonesia, Journal of Geophysical Research, Vol. 116,
doi:10.1029/2011JB008253.
Mansinha, L. and D. E. Smylie (1971): The displacement fields of inclined faults, Bulletin of the
Seismological Society of America, Vol. 61, No. 5, pp. 1433-1440.
Matsumoto, T., K. Hashi, F. Imamura and N. Shuto (1998): A Development of a Numerical Model of
Two Layers Flow to Simulate a Tsunami Generation Caused by a Debris Flow, Proceedings of
Coastal Engineering, JSCE, Vol. 45, pp. 346-350 (in Japanese).
http://library.jsce.or.jp/jsce/open/00008/1998/45-0346.pdf
Matsuyama, M., M. Ikeno, T. Sakakiyama, K. Yanagisawa and N. Fujii (2005): Study on Wave
Breaking Criterion of Tsunami Soliton Fission Based on Undistorted Experiment, Annual
Journal of Coastal Engineering, JSCE, Vol. 52, pp. 241-245 (in Japanese).
http://library.jsce.or.jp/jsce/open/00008/2005/52-0241.pdf
Matsuyama, M., M. Ikeno, T. Sakakiyama and T. Takeda (2006): Wave Breaking Model after Soliton
Fission on a Continental Shelf in Tsunami Numerical Simulation, Annual Journal of Coastal
Engineering, JSCE, Vol. 53, pp. 226-230 (in Japanese).
http://library.jsce.or.jp/jsce/open/00008/2006/53-0226.pdf
McLeod, P., S. Carey and R. S. J. Sparks (1999): Behaviour of particle-laden flows into the ocean:Experimental simulation and geological implications, Sedimentology, Vol. 46, pp. 523–536.
Nagano, O., F. Imamura and N. Shuto (1989): Numerical Simulation of the Chilean tsunami in thearea along the shore, Proceedings of Coastal Engineering, JSCE, Vol. 36, pp. 183-187 (inJapanese).
http://library.jsce.or.jp/jsce/open/00008/1989/36-0183.pdf
National Astronomical Observatory of Japan (2007): Chronological Scientific Tables 2008, Maruzen
Publishing Co., Ltd., 278p. (in Japanese).
Nishimura, S., M. Ando and S. Miyazaki (1999): Inter-plate Coupling Along the Nankai Trough andSoutheastward Motion Along Southern Part of Kyushu, Journal of the Seismological Societyof Japan. 2nd ser., Vol. 51 (1998-1999), Issue 4, pp. 443-456 (in Japanese).
https://www.jstage.jst.go.jp/article/zisin1948/51/4/51_4_443/_pdf/-char/en
Okada, Y. (1985): Surface deformation due to shear and tensile faults in a half-space, Bulletin of the
Seismological Society of America, Vol. 75, No. 4, pp. 1135-1154.
Omote, T. (1946): The Tsunami, the Earthquake Sea Waves, that Accompanied the Great Earthquakeof Dec. 7, 1944, Bulletin of the Earthquake Research Institute, University of Tokyo, Vol. 24(1Appendix 4- 125

4), pp. 31-57 (in Japanese).
https://repository.dl.itc.utokyo.ac.jp/?action=repository_uri&item_id=34294&file_id=19&file_no=1
Peregrine, D.H. (1967): Long waves on a beach, Journal of the Fluid Mechanics, Vol. 27, Part4, pp.
815-827.
Pham, V.P., M. Hasebe and I. Takahashi (2012): A Study on Three-Dimensional Tsunami Analysis
Using VOF Method, Journal of Japan Society of Civil Engineers, Ser. B2 (Coastal
Engineering), Vol. 68, No. 2, pp. I_071-I_075 (in Japanese).
Sagiya, T. (1999): Interplate coupling in the Tokai District, Central Japan, deduced from continuous
GPS data, Geophysical Research Letters, Vol. 26, No. 15, pp. 2315-2318.
Sasahara, N. (2004): Numerical Simulation of the Tsunami caused by the sector Collapse of
Mt.Mayuyama, Shimabara Peninsula, Kyushu in 1792, REPORT OF HYDROGRAPHICAND OCEANOGRAPHIC RESEARCHES No.40 March,
http://www1.kaiho.mlit.go.jp/GIJUTSUKOKUSAI/KENKYU/report/rhr40/rhr40-02.pdf
Satake, K., M. Okada and K. Abe (1988): Tide gauge response to tsunamis: Measurements at 40 tidegauge stations in Japan, Journal of Marine Research, Vol. 46, pp. 557-571.
Satake, K. (1991): Recent Studies on Tsunamis, Journal of the Seismological Society of Japan. 2ndser., Volume 44 (1991) Issue Supplement, pp. 99-112 (in Japanese).
https://www.jstage.jst.go.jp/article/zisin1948/44/Supplement/44_Supplement_99/_pdf/char/en
Satake, K. and Y. Kato (2001): The 1741 Oshima-Oshima Eruption: Extent and Volume of Submarine
Debris Avalanche, Geophysical Research Letters, Vol. 28, No. 3, pp. 427-430.
Satake, K. and Y. Kato (2002): The 1741 Kanpo-Tsunami Occurred Because of Sector Collapse of
Oshima-Oshima, Monthly Kaiyo No. 28, pp. 150-160 (in Japanese).
Satake, K., J.R. Smith and K. Shinozaki (2002): Three-Dimensional Reconstruction and Tsunami
Model of the Nuuanu and Wailau Giant Landslides, Hawaii, in Hawaiian Volcanoes: Deep
Underwater Perspectives, edited by Takahashi et al., AGU Geophysical Monograph, 128, pp.
333-346.
Satake, K. (2007): Volcanic origin of the 1741 Oshima-Oshima tsunami in the Japan Sea, Earth Planets
Space, Vol. 59, pp. 381-390.
Sato, S. (1995): Numerical Computation of the Tsunami in Consideration of Division and Breaking
Wave, Proceedings of Coastal Engineering, JSCE, Vol. 42, pp. 376-380 (in Japanese).
http://library.jsce.or.jp/jsce/open/00008/1995/42-0376.pdf
Sato, T., R. W. Graves and P. G. Somerville (1999): Three-dimensional finite-difference simulationsof long-period strong motions in the Tokyo metropolitan area during the 1990 Odawara
earthquake (MJ 5.1) and the great 1923 Kanto earthquake(MS 8.2) in Japan, Bulletin of the
Appendix 4- 126

Seismological Society of America, Vol. 89, No. 3, pp. 579-607.
Sayama, J., T. Goto and N. Shuto (1986): Error of the Tsunami Numerical Computation about theRefraction, Proceedings of Coastal Engineering, JSCE, Vol. 33, pp. 204-208 (in Japanese).
http://library.jsce.or.jp/jsce/open/00008/1986/33-0204.pdf
Shibaki, H., T. Mikami and T. Goto (1994): Propagation characteristics of Hokkaido Nansei-Oki
Earthquake Tsunami, Proceedings of Coastal Engineering, JSCE, Vol. 41, pp. 226-230 (inJapanese).
http://library.jsce.or.jp/jsce/open/00008/1994/41-0226.pdf
Shuto, N. (1986): TSUNAMIS AND COUNTERMEASURES, Journal of Japan Society of Civil
Engineers, Volume 1986, Issue 369, pp. 1-11 (in Japanese).
https://doi.org/10.2208/jscej.1986.369_1
Shuto, N. and M. Uhana (1995): The run-up heights for the 1994 Hokkaido Toho-Oki earthquake
tsunami, Research Report of Tsunami Engineering Vol.12, Part 2, p. 1 (in Japanese).
http://www.tsunami.civil.tohoku.ac.jp/hokusai3/J/publications/pdf/vol.12_7.pdf
Steketee, J.A. (1958): On Volterra's dislocations in a semi-infinite elastic medium, Canadian Journalof Physics, Vol. 36, pp. 192-205.
Suzuki, H. (2002): Underground Geological Structure beneath the Kanto Plain, Japan, Report of the
National Research Onstitute for Earth Science and Disaster Prevention, Vol. 63, pp. 1-19 (inJapanese).
http://dil-opac.bosai.go.jp/publication/nied_report/PDF/63/63suzuki.pdf
Takahashi, K. and T. Tomita (2013): Simulation of the 2011 Tohoku Tsunami in Kuji Bay Using ThreeDimensional Non-Hydrostatic Numerical Model, Journal of Japan Society of Civil Engineers,
Ser. B2 (Coastal Engineering), Vol. 69, No. 2, pp. I_166-I_170 (in Japanese).
Tanaka, H. (1985): Development of Mathematical Models for Tsunami Behavior on Coastal Zones,
CRIEPI Research Report, No. 385017 (in Japanese).
http://criepi.denken.or.jp/jp/kenkikaku/report/detail/385017.html
Tomita, T. and T. Kakinuma (2005): Storm Surge and Tsunami Simulator in Oceans and Coastal Areas(STOC), Report of the Port and Airport Research Institute, Vol. 44, No. 2, pp. 83-98 (inJapanese).
Tomita, T. and K. Honda (2008): Application of Three-Dimensional Non-Hydrostatic Numerical
Model to Tsunamis in Coastal Areas, Proceedings of Coastal Engineering, JSCE, Vol. 55, pp.
231-235 (in Japanese).
Tonomo, K., T. Shikata and Y. Murakami (2015): ACCURACY STUDY OF NUMERICALSIMULATION OF TSUNAMI APPLIED TO THE SUBMARINE LANDSLIDE MODEL,
Journal of Japan Society of Civil Engineers, Ser. B3 (Ocean Engineering), Volume 71 (2015),
Issue 2, pp. 557-562 (in Japanese).
Appendix 4- 127https://doi.org/10.2208/jscejoe.71.I_557
Tsuchiya, S., Y. Satou, M. Matsuyama and Y. Tanaka (2013): The Effect Generated by Calculation
Method of the Sea Bottom Displacement on Tsunami Estimation - Three-dimensional Sea
Bottom Crustal Movement Analysis -, Journal of Japan Society of Civil Engineers, Ser. B2(Coastal Engineering), Volume 69 (2013), Issue 2, pp. I_441-I_445 (in Japanese).
https://doi.org/10.2208/kaigan.69.I_441
Tsunami Evaluation Subcommittee, The Nuclear Civil Engineering Committee, JSCE (2002):
Tsunami Assessment Method for Nuclear Power Plants in Japan.
http://committees.jsce.or.jp/ceofnp/system/files/JSCE_Tsunami_060519.pdf
Tsunami Evaluation Subcommittee, The Nuclear Civil Engineering Committee, JSCE (2007):RESEARCHFOR

DEVELOPINGTSUNAMIEVALUATIONMETHODS–PROBABILISTIC TSUNAMI HAZARD ANALYSIS /NUMERIAL SIMULATIONMETHODS WITH DISPERSION AND WAVE BREAKING, Journal of Japan Society of Civil
Engineers, Ser. B, Vol. 63, No. 2, pp. 168-177 (in Japanese).
https://www.jstage.jst.go.jp/article/jscejb/63/2/63_2_168/_pdf/-char/ja
Watts, P., S. T. Grilli, D. R. Tappin and G. J. Fryer (2005): Tsunami Generation by Submarine Mass
Failure II: Predictive Equations and Case Studies, Journal of Waterway, Port, Coastal, andOcean Engineering, 131:6(298), 298-310.
Yamada, N. and H. Yamanaka (2003): Ground Motion Simulations of Moderate Earthquakes for
Comparison of Performance of 3D Subsurface Structural Models in Kanto Plain for Strong
Motion Prediction, Journal of the Seismological Society of Japan. 2nd ser., Volume 56 (20032004), Issue 2, pp. 111-123 (in Japanese).
https://www.jstage.jst.go.jp/article/zisin1948/56/2/56_2_111/_pdf/-char/en
Yanagisawa, H., A. Aoki, K. Sassa and K. Inoue (2014): Numerical Simulation of 1792 Ariake-Kai
Tsunami using Landslide-Tsunami Model, Journal of Japan Society of Civil Engineers, Ser. B2(Coastal Engineering), Volume 70 (2014), Issue 2, pp. I_151-I_155 (in Japanese).
https://doi.org/10.2208/kaigan.70.I_151
Yoneyama, N., H. Nagashima and K. Toda (2008): Numerical Analysis for the Behavior of the Driftage
with Tsunami Run-up Using FAVOR Method, Annual Journal of Hydraulic Engineering, Vol.
52, pp. 1399-1404 (in Japanese).
Yoneyama, N. and H. Nagashima (2009): Development of a Three-Dimensional Numerical Analysis
Method for the Drift Behavior in Tsunami, Journal of Japan Society of Civil Engineers, Ser. B2(Coastal Engineering), Vol. B2-65, No. 1, pp. 266-270 (in Japanese).

Appendix 4- 128

Chapter 5. Probabilistic Assessment Methods
5.1. Standard deviation and truncation threshold of estimation error
5.1.1. Statistics of variance between calculation results and run-up height records of tsunami
To view the statistical properties of variance between calculation results by tsunami simulationand the run-up height records of tsunami, the results of calculations simulating 10 historical earthquake
tsunami (total of 1,505 trace points), which are given in Table 5.1.1-1, have been analyzed in two
patterns:• Difference between the run-up height records and calculated value• Ratio of run-up height records to calculated value (logarithm).
The results are shown in Figure 5.1.1-1. However, both are also displayed using a 1:18 scale
factor for standard deviation for all data along the vertical access.
When the data given in Figure 5.1.1-1 are expressed as a distribution of the frequency of thedifference or ratio (logarithm) for each representation, the diagram given in Figure 5.1.1-2 is yielded.
The chi-square test for normality is carried out. The result is as shown in Table 5.1.1-2 and thislogarithm is closer to the normal distribution. In other words, the ratio of the run-up height records tocalculated value generally conforms to the logarithmic normal distribution.

Table 5.1.1-1 Fault models and number of data
Earthquake Tsunami

Number of Data

1707 Hoei

61

1854 Ansei-Tokai

88

1854 Ansei-Nankai

60

1896 Meiji-Sanriku

83

1933 Showa-Sanriku

325

1944 Tonankai

41

1946 Nankai

149

1968 Tokachi-Oki

273

1983 Nihonkai-Chubu

209

1993 Hokkaido Nansei-Oki

216

Total

1,505

Note) restricted tsunami height estimations below 12m.

Appendix 5- 1

Run-up height records-Calculated value (m)Distribution of (run-up height records - calculated value)

Calculated value (m)log(TRun-up height records/ Calculated value)

Distribution of log(run-up height records/calculated value)

Calculated value (m)Figure 5.1.1-1 Scatter diagram of run-up height records and calculated values

Appendix 5- 2

Range (m)Frequency distribution of (run-up height records - calculated value)

Frequency

Range

Frequency distribution of log (run-up height records/calculated value)

Frequency

Figure 5.1.1-2 Histogram of run-up height records and calculated values

Table 5.1.1-2 χ2 test of fitness to normal distribution
χ2 -value

Resulttrun-up height records-calculated value

393.53NGlog(run-up height records-calculated value)

226.09OK

TypeNote) The range of mean ± 2.3×S.D. is divided into 200 sections in the test. OK means that the null
hypothesis "Data follow a normal distribution" is not rejected with significant level 5%. (Thecritical value of χ2 distribution for the P-value, 0.05, conducting the right-tailed test is 235 incase of 201 DOF. If χ2 value greater than the critical value, the hypothesis is rejected.)

Appendix 5- 3

5.1.2. Examination of variance in estimated tsunami heights
With respect to the variance in calculations of tsunami height using in PTHA, an attempt wasmade to ascertain the extent of variance in numerical simulations of the 2011 off the Pacific coast of
Tohoku Earthquake (2011 Tohoku earthquake).
The Cabinet Office’s inversion model (see Figure 5.1.2-1), which is able to provide a good
representation of tsunami traces, was used to perform a numerical simulation of the 2011 Tohoku
Earthquake. Distributions of the ratio of observed values to calculated values (“O/C”) were examinedaccording to the degree of data reliability and distance from the coastline.
The Japanese main island of Honshu was the only region examined, and the minimum grid sizefor the coastal region was set at 50m.
The O/C distribution, which only used tsunami trace data of reliability level A, is shown in Figure
5.1.2-2. In the diagram, the boundary from the geometric mean to the nth factor of standard deviation
is indicated by a broken line. There are no results that exceed the mean+4β. There are some points
where the mean+3β is exceeded, but, the following two phenomena arose, as shown in Figures 5.1.23 through 5.1.2-5, with regard to these locations where O/C significantly deviates.
• Although the calculation results are generally constant, the observed values differ significantly
only for the locations in question.
• Although the observed values are generally constant, the calculated values differ significantly
only for the locations in question.
It is surmised that it is likely both of these cases originate in the reproducibility of topographyusing 50-m grids, and it would be difficult for such phenomena to occur in cases where the grid size
is narrowed down, such as in tsunami assessments for nuclear power plants.
In Figure 5.1.2-6, the ratio of number of data where the mean±nβ is exceeded to total number ofdata (Cabinet Office model; only Honshu) is shown. Here, the theoretical value of the probability thatthe truncation threshold of the logarithmic normal distribution may be exceeded is shown in Table
5.1.2-1. The ratio of O/C exceeding the mean±nβ in the numerical simulation results was confirmed
to consistent generally with the theoretical exceedance probability of the logarithmic normal
distribution.
When setting the truncation threshold for the tail of the logarithmic normal distribution, theaforementioned examination results may be used as a reference.

Appendix 5- 4

Num. of blocks:98
Num. of subfaults:4,575

49.6m

Figure 5.1.2-1 Cabinet Office’s inversion model

断層モデル：内閣府モデル／痕跡データ：信頼度Ａのみ (n=2782)(N=2782)

10.0

Observed/ Calculated
観測値／計算値

Izumi-machi,,Iwaki, Fukushima

Geometric mean: 0.956
Geometric S.D.: 0.295(κ:1.34)

Ohfunato-ko, Ohfunato

Distancefrom coastline: 0 – 100m
海岸線からの距離：0～100m
Distancefrom coastline: 100 – 200m
海岸線からの距離：100～200m
Distancefrom coastline: 200 – 500m
海岸線からの距離：200～500m
1.0Distancefrom coastline: 500 – 1000m
海岸線からの距離：500～1000m
±１β
±２β
±３β
±４β

Oirase, Aomori
Miyatojima, Higashimatsushima, Miyagi
0.1
34.0

35.0

36.0

37.0

38.0

39.0

40.0

41.0

42.0

Latitude(deg.)
緯度（°）

Figure 5.1.2-2 The O/C distribution, which only used tsunami trace data of reliability level A(Cabinet Office model; only Honshu)

Appendix 5- 5

Figure 5.1.2-3 Tsunami trace points in Izumi-machi, Iwaki, Fukushima (Reliability; A, No.690)

Appendix 5- 6

Obs. : 8.8m
Cal. : 6.3m
4228

Obs. : 9.5m
Cal. : 3.3m

4227

Obs. : 8.1m
Cal. : 5.8m
4225
4226

Obs. : 9.3m
Cal. : 4.0m

Figure 5.1.2-4 Tsunami trace points in Ohfunato-ko, Ohfunato (Reliability: A, No.4227)

Appendix 5- 7

Figure 5.1.2-5 Tsunami trace points in Miyatojima, Higashimatsushima, Miyagi(Reliability: A, No.187)

Appendix 5- 8

Table 5.1.2-1 Theoretical probability to exceed the truncation threshold of normal distribution
Truncation threshold

Exceedance probability (%)

mean±1β15.866mean±2β2.275

mean±2.3β

1.072

mean±3β0.135

mean±4β0.003

Cabinetoffice'sfault /model/ tsunami
tracerecords:
height :reliability
reliability
A (N=2782)
Cabinetoffice’sfault modeltsunamirun-up height
A (N=2782)
18

Exceedance ratio (%)

16
14

13.6
13.4

12
10

plus side8

minus side

6

3.9

4
2

1.2

0
±１β

Theory

2.6

1.9
±２β

0.6

0.0 0.1

±３β

±４β

0.2

±2.3β

Range of variation
Figure 5.1.2-6 Ratio of the number of data to exceed the meannβ to total number of data
(Cabinet office’s fault model; only Honshu)
The followings are examples of truncation thresholds configured for the logarithmic normal
distribution.
[1] Atomic Energy Society of Japan (2015): Upper limit truncation for seismic ground motion• “Ground motion intensity is phenomenally finite. Accordingly, the range in which thelogarithmic normal distribution is valid needs to be configured to be finite, so a truncationthreshold is set. In cases where a sufficient basis cannot be obtained for setting a truncationthreshold, the range of the level of ground motion acceleration, which affects core damage
frequency, may be taken into consideration and the truncation threshold set at a sufficiently
large value (for example, up to five times the standard deviation)”.
• “The truncation threshold of the logarithmic normal distribution was a uniform distribution

Appendix 5- 9

within a range from ±2.0σ to ±4.5σ”.
[2] Japan Nuclear Energy Safety Organization (2014): Setting truncation for logarithmic normal
distribution in a tsunami propagation model• “For example, in cases where a ‘phenomenon, in which 1% is reached on both sides of the
distribution, does not actually occur,’ 1% is the cutoff on both sides of the distribution”(Truncation at =2.3β).
[3] National Research Institute for Earth Science and Disaster Prevention (2005): Truncation of thetail of the distribution in an examination of methods for the National Seismic Hazard Maps forJapan• “In cases where the target is up to a level of probability where there is a 5% probability ofexceedance in 50 years or a 3% probability of exceedance in 30 years… what is considered tohave a substantial impact on the results is a range within +2σ. Based on this, data fromobservation records that exceeds a range of ±3σ is regarded as statistical outliers, and the tailof the logarithmic normal distribution is truncated along this range”.
5.2. Previous studies about the b value in the G-R equation
When focusing on multiple earthquake swarms, the G-R model assumes that:log n  a  bM
holds between magnitude M and the number of earthquakes n for each magnitude (hereinafter, thisexpression is referred to as the “G-R equation”). Here, the b value may be found by applying the G-R
equation to statistics for earthquakes that occur in sea regions, which are the objects of the assessment,
and, in cases where the b value included in the G-R equation is 1, it signifies that, when the magnitude
increases 1, the number of earthquakes will be 1/10 the magnitude.
The b value varies depending upon the sea regions that is targeted. Ogata (2015) showed the bvalue distribution globally, and stated that, broadly speaking, the b value was larger along oceanic
ridges and smaller in subduction zones, and that the regional characteristics are quite detailed whenviewed in more detail.
In formulating a nationwide seismic ground motion prediction map, the Headquarters for
Earthquake Research Promotion (2013) assessed the probability distribution of earthquake magnitude
on the assumption that the distribution observed the relationship in the G-R model, which has amaximum value, and used 0.9, which is considered to be the mean for the b value for the area around
Japan. In addition, it has been pointed out that the b value also varies over time in response to seismic
cycles. For example, Kusuki et al. (2011) observed a decline in the b value before the main shock forthe source region of the 2011 Tohoku earthquake.

Appendix 5- 10

5.3. Effect of storm surge on Probabilistic Tsunami Hazard Analysis
5.3.1. Objectives
In a Probabilistic tsunami hazard analysis, the distribution of the probability of exceedance of thetsunami tide level is found by combining (convoluting) the tsunami height distribution and the tidelevel distribution in order to find the probability that the tide level will be exceeded at a power
generation facility.
This tide level distribution is prepared using any of the following:• Prepared by means of statistical processing using records of tide measurements around the power
generation facility• Artificially calculated using the harmonic constant
The issue when using a tide level distribution is the possibility that, storm surges and otherphenomena that “have a low occurrence frequency, but a large tide level deviation when they occur”
may not be sufficiently reflected. In this examination, we focus on storm surge, which is assumed tohave the largest impact except for tsunamis, and we evaluate impact of storm surge deviation on a
Probabilistic tsunami hazard analysis.
5.3.2. Design of probabilistic typhoon models(1) Data used for statistical analysis
The typhoon for probabilistic model design is extracted from the Japan Meteorological Agency
Best Track Data for the period from 1951 to 2005.
(2) Formulation
1) Typhoon occurrence
The number of typhoons occurring during a one-year period is modeled as a Poisson
distribution for each period of time. In other words, in cases where the average number oftyphoons occurring during the one-year period is λ, then the probability of n typhoons
occurring during a one-year period is given with the following equation.

f (n) e   nn!

The locations where typhoons occur and central pressure when they occur are assumed tofollow the cumulative frequency distribution set by the observation data.
2) Time evolution of Typhoon
The time evolution for the probabilistic typhoon model is determined in the following
Appendix 5- 11

manner using the autoregressive process (AR) model.

pi  pi 1  pi xi  xi 1  vi dt
pi  pi  pivi  vi  vi
pi is the central pressure, xi is the central coordinates of the typhoon, and vi is the velocity at
which the typhoon travels. The degree to which the central pressure changes is calculated using
the sum of the mean field (Δpi) and deviation δpi at the point where the typhoon is situated,and velocity vi, which is rate at which the coordinates change, is also calculated using the sumof the mean field (vi) and deviation δvi. Deviation is expressed by the following autoregressive
process model:pi  a1pi 1  a2pi  2  a3pi 3   p








vi  A1vi 1  A2vi  2   v
The order of the autoregressive process model is determined by trial and error, so there isroom for optimization. The coefficient of the autoregressive process model is determined bymultiple linear regression analysis using past observation data. Velocity coefficients A1and A2
are 2 x 2 matrices. εp and εv indicate random errors, and are given using a normal distributionof mean 0. Variance of the normal distribution is the mean of the sum of squared errors between
observation data and the given regression equation.
3) Configuration of typhoon radius
The shape of a developed typhoon is almost circular. For this reason, in the cases where
the central pressure and the typhoon radius are given, a simplified approach has been proposed
for finding the gradient wind distribution and the pressure distribution on land by assuming a
concentric distribution (there are also cases where an elliptical distribution is assumed). This
examination uses the typical Myers equation to find the pressure decrease. The pressure, atpoints that are r distance away from the typhoon center, is approximated using the following
equation: r p  pc  (1010  pc ) exp  0 
 r
pc is the central pressure and r0 is the typhoon radius.
(3) Calculation of storm surge deviation
In this examination, the storm surge deviation is calculated with the following simplified
equation, which is published in the Tide Table (2003 edition):H  a (1010  P )  bW cos   c

P is the minimum pressure (hPa), W is the maximum wind velocity, and θ is the angle formed by
Appendix 5- 12the harbor and wind direction. The coefficients a, b, and c of the simplified equation have been
given for major harbors in Japan based on statistics for the past storm surges.
1) Results• Typhoon track distribution
Figure 5.3.2-1 shows the results of a probabilistic typhoon model that was run for aperiod of 100 years to generate typhoon tracks. It was found that the generated typhoon
tracks correspond to the distribution of tracks from observation data.

Figure 5.3.2-1 Generated typhoon track over a period of 100 years2) Minimum pressure distribution
Figure 5.3.2-2 shows the distribution of minimum pressure over a period of 100 years,
which was generated using a probabilistic typhoon model.

Appendix 5- 13

Figure 5.3.2-2 The distribution of minimum pressure over period of 100 years, generated using aprobabilistic typhoon model (hPa)
5.3.3. Calculation of typhoon theoretical maximum intensity
In this section, we calculate probabilistic typhoons over a long period of 1,000 years in order toexamine the effect of storm surge on hazard analysis. However, in the formulation of probabilistic
typhoons as previously described, powerful typhoons occur that appear to be unrealistically extreme.
Accordingly, the limit of the physical development of tropical cyclones is calculated in accordancewith the characteristics of the meteorological field during each period of time, and this is used as thelimit for development in the probabilistic typhoon model.
The Maximum Potential Intensity of typhoons is calculated with reference to Holland (1997),
and the surrounding meteorological conditions are used to find the pressure of the typhoon center bymeans of iterative calculation. For the meteorological data used in calculating the maximum typhoon
intensity, the NCEP/NCAR re-analysis data is used for three variables: vertical profile of temperature,temperature near land surface, and sea level pressure.
5.3.4. Effect of storm surge on tsunami hazard analysis(1) Assessment procedure
In a standard tsunami hazard assessment, the tide level deviation in front of a site is foundby superimposing the distribution of tsunami deviation which assumes a logarithmic normal
distribution onto the tide level distribution, which is prepared based upon tide measurement
records and other sources. Since the objective of this examination is to assess the effect that
abnormal tide levels due to typhoon have on a tsunami hazard analysis, the tide level distribution
Appendix 5- 14

is expressed by combining astronomical tide levels and storm surge deviation. Of these, theastronomical tide levels are prepared artificially by using a harmonic constant, and the storm
surge deviation is found by using the probabilistic typhoon model (Inoue et al., 2013).
(2) Case studies of configuration of astronomical tide levels
An artificial tide level distribution is prepared using the harmonic constant published in the2007 edition of the Tide Table. The prepared tide level distribution is combined with the tide level
deviation prepared using the probabilistic typhoon model.
Using harmonic analysis, the astronomical tide level is represented by linear superpositionof trigonometric function. Tide level η(t) for time t at a certain point is calculated using thefollowing equation:
 2t  i   i  Ti (t )   H i cosiwhere, Hi is the amplitude of the tidal constiuent components, and Ti is the inherent period. μi is
known as the phase angle, which expresses the difference in phase of the tide producing force
itself. This is a constant that does not depend upon the location point. κi is known as the lag angle
and indicates the shift in phase determined for each location point.
(3) Assessment of effect of storm surge deviation on tide level distribution
The probabilistic typhoon model is used to assess the effect of storm surge deviation on tidelevel distribution. For the distribution of the astronomical tide levels, two locations, Nagoya(representing the Pacific Ocean side) and Maizuru (representing the Japan Sea side) are used. In
running the probabilistic-model, the following procedures are used:• Three time periods are covered: 10 years, 100 years, and 1,000 years,• Random numbers are varied and 10 trial calculations conducted for each time period.
First, a distribution of tide levels is prepared, which combines astronomical tide levels andstorm surge deviation, to investigate the relative impact of storm surge. The probability density
function of the combined tide levels is found by finding the probability density function of theastronomical tide levels and storm surge deviation and then calculating their convolution. Figure
5.3.4-1 shows results indicating the probability of exceedance calculated based upon theprobability density function. The red line is the distribution in a case where storm surge is notincluded, and the black lines are the results after adding storm surge based on the probabilistic
typhoon model (10 trial calculations). The calculation results are able to verify the following
properties.
[1] A noticeable difference in the distribution profile emerges in the case of probability smaller
than 10-3.
Appendix 5- 15

[2] It is found that lengthening the calculation period of the probabilistic typhoon model is able
to suppress variance, which typhoons have, and make a more reliable assessment.

Figure 5.3.4-1 Exceedance probability distribution of astronomical tide levels and storm surge
deviation on Nagoya and Maizuru(10 trial calculations with probabilistic typhoon model for 10years, 100 years, and 1000
years)(4) Assessment of effect on hazard analysis of case where tsunami height is assumed
In tsunami hazard analysis, a tsunami height distribution is often used that truncates the edge
Appendix 5- 16

of the logarithmic normal distribution so that various types of errors that occur in numericalsimulations of tsunami may be taken into account. Accordingly, the impact of storm surge is
examined for a case where the truncated height of the distribution and the magnitude of variancein the distribution are varied and superimposed on the tide level.
• Tsunami height median value (μ): 5m, 1m• Variability (κ): 1.25, 1.45
• Truncated water level (σco): 2.3σ, 10σ
Figure 5.3.4-2 shows the probability density function and probability of exceedance in a casewhere the median value of the tsunami height is set at 5m.

Figure 5.3.4-2 The probability density function (Left) and exceedance probability (Right) in a cases
where the median value of the tsunami height is set at 5m
Figures 5.3.4-3 and 5.3.4-4 show the exceedance probability of the tide level when a tsunami
occurs is found based upon the aforementioned conditions. The following properties are observed.
1) Case where the truncated water level is 2.3σ
• The impact of storm surge occurs at a probability of 10-5~10-7 (Table 5.3.4-1).
-> If it is assumed that a tsunami occurs once every 100 years, then the occurrence
frequency ranges from 10-7 times/year to 10-9 times/year, so the impact of storm surge
does not pose an issue at a level covered in a typical tsunami hazard analysis.
• The higher the tsunami height is, the less effect storm surge has.
• The greater the variance in tsunami is, the less effect storm surge has.
2) Case where the truncated water level is 10σ• If tsunami height is equal or larger than storm surge deviation, then the effect of storm
surge may be almost completely disregarded.
• If tsunami height is smaller than storm surge deviation, then the tide level is exceeded,
but the storm surge effect is small.

Appendix 5- 17

Figure 5.3.4-3 Tide level exceedance probability distribution when a tsunami occurs on Nagoya(Truncation water level: 2.3σ(Left), 10σ(Right))

Appendix 5- 18

Figure 5.3.4-4 Tide level exceedance probability distribution when a tsunami occurs on Maizuru(Truncation water level: 2.3σ (Left), 10σ (Right))

Appendix 5- 19

Table 5.3.4-1 Frequency which storm surge effects on to tsunami hazard analysis (exponential
notation)

Tsunamiheight5m
Nagoya1m
5m
Maizuru
1m

Truncated water level with
Variability

logarithmic normal distribution

2.3σ

10σ

κ=1.25-6-

κ=1.45-6.5-

κ=1.25-5-5

κ=1.45-5.5-

κ=1.25-6-

κ=1.45-6.5-

κ=1.25-5-

κ=1.45-5.5-

5.3.5. Summary
A study using the probabilistic typhoon model has been able to verify that the effect of storm
surge due to a typhoon on tsunami hazard analysis is very small with the exception of special cases. It
is found that the effect of storm surge is relatively large in:• Cases where tsunami height is small in comparison to the storm surge deviation• Cases where variance in tsunami height is small
Also, the degree of storm surge effect varies also depending upon the truncated water level of thetsunami height distribution. It is found that the greater the truncated tsunami height is and the closer it
is to the logarithmic normal distribution, the smaller the effect of storm surge is which is offset byerror in the tsunami simulation.

[Appendix 5 References]
Atomic Energy Society of Japan (AESJ) (2015): A Standard for Procedure of Seismic Probabilistic
Risk Assessment for Nuclear Power Plants, AESJ-SC-P006:2015, pp. 374-375 (in Japanese).
Atomic Energy Society of Japan (AESJ) (2015): A Standard for Procedure of Seismic Probabilistic
Risk Assessment for Nuclear Power Plants, AESJ-SC-P006:2015, 426p. (in Japanese).
Atomic Energy Society of Japan (AESJ) (2015): A Standard for Procedure of Seismic Probabilistic
Risk Assessment for Nuclear Power Plants, AESJ-SC-P006:2015, 60p. (in Japanese).
Headquarters for Earthquake Research Promotion (2013): Study on ground motion hazard assessment
Appendix 5- 20

of future (in Japanese).
http://www.jishin.go.jp/evaluation/seismic_hazard_map/shm_report/shm_report_2013
Holland, G. J. (1997): The Maximum Potential Intensity of Tropical Cyclones, Journal of the
Atmospheric Sciences, vol. 54, No. 21, pp. 2519-2541.
Inoue, T., N. Fujita, M. Matsuyama, and Y. Tanaka (2013): A STUDY ON THE SIMULTANEOUS
OCCURRENCE PROBABILITY OF TSUNAMI AND STORM SURGE, Journal of Japan
Society of Civil Engineers, Ser. B3 (Ocean Engineering), Volume 69 (2013) Issue 2, pp.
I_425-I_430 (in Japanese).
https://www.jstage.jst.go.jp/article/jscejoe/69/2/69_I_425/_pdf/-char/en.
Iwabuchi, Y., H. Sugino, and K. Ebisawa (2014): Guidelines for Developing Design Basis Tsunami
based on Probabilistic Approach, Japan Nuclear Energy Safety Organization, JNES-RE-20132041 (in Japanese with English abstract).
Nanjo, K.Z., N. Hirata, K. Obara, and K. Kasahara (2011): Spatiotemporal change in b values aroundthe hypocenter of the 2011 Tohoku-Oki earthquake, Report of the Coordinating Committee for
Earthquake Prediction, Japan, Vol. 86, 3-17, pp. 121-122 (in Japanese).
http://cais.gsi.go.jp/YOCHIREN/report/kaihou86/03_17.pdf.
National Research Institute for Earth Science and Disaster Prevention, Japan (2005): A Study on
Probabilistic Seismic Hazard Maps of Japan, Technical Note of the National Research Institutefor Earth Science and Disaster Prevention No. 275 (in Japanese).
http://dl.ndl.go.jp/view/download/digidepo_9682770_po_n275.pdf?contentNo=1&alternative
No=.
Ogata, Y. (2015): Stochastic Prediction of Earthquakes - A Strategy for the Research, Proceedings ofthe Institute of Statistical Mathematics Vol. 63, No. 1, pp. 3–27 (in Japanese).
http://www.ism.ac.jp/editsec/toukei/pdf/63-1-003.pdf.

Appendix 5- 21

Chapter 6. Examples of Applications of Deterministic Hazard Analysis“Notes: Examples of Applications of Deterministic Hazard Analysis”
The examples of applications of deterministic tsunami hazard analysis, which are presented inthis chapter, are premised on tsunami source locations, intensity and other characteristics given as
conditions, and illustrate the procedures and results of parametric studies for taking into accountuncertainty and configuration of the standard fault models presented in Chapter 4 of the main volume.
In accordance with the aforementioned purpose, it should be kept in mind that these application
examples neither specify in detail the causes, locations, intensities or other characteristics of tsunamithat may occur in the future nor negate other assessment procedures. Also, the parameters and otherinformation presented in these application examples are entirely illustrative. In actual deterministic
tsunami hazard analyses, sufficient consideration needs to be given to the appropriateness ofparameter configurations and other elements in the analysis.

Covering the sea region extending from the Kuril-Kamchatka Trench to the Japan Trench, an
example is presented of a deterministic tsunami hazard analysis based upon a method for considering
uncertainty, which takes into account knowledge gained from the 2011 Tohoku earthquake.
6.1. Basic matters(1) Examination method
The examination method is given in Table 6.1-1. First, the standard fault model is preparedbased upon tectonic data and other information about the target region. Next, as described in
section 4.2.3.1(1) of the main volume, a simplified parametric study is carried out of major factors,
and the locations of large slip areas, which significantly affect the region assessed, are selected.
Lastly, a detailed parametric study is conducted of subordinate factors, and the effect of
uncertainty is studied as concerns kinematic parameters of fault rupture.

Appendix 6- 1

Table 6.1-1 Investigation method for the sea area along the Kuril trench and the Japan trench
StepContent

Remarks

1. standard fault model

Large slip area and super large slip area are modeled underthe method proposed by Cabinet office.

-2. Simplified parametric
study

Overlap the half of the large slip area with the next fault
model. (Seto and Takahashi, 2014)

3. Detailed parametric study

Rupturevelocity

1.0km/s, 2.0km/s,
2.5km/s, 3.0km/s

Hypocenter

Setting 6 points along the outerborder of large slip area and in the
super large slip area

Rise time

30s, 60s, 180s, 300s

Rise time: 30s
Rupture velocity: ∞Rise time:30s(fixed vale)
Rupture velocity: ∞,2.5km/s(2) Analysis conditions for the numerical simulation
The analysis conditions used in the numerical simulation of tsunami are given in Table 6.12.

Table 6.1-2 Analysis condition
Specification

Description

Calculation area

Pacific ocean from northern Kuril islands to Boso peninsula

Calculation mesh grid size

Offshore 1,350m, 450m, 150m, coastal area 50m

Basic equation
Initial displacement of sea
bottomNonlinear long wave theory

Boundary condition
Overflow condition
Horizontal eddy viscosity
coefficient

The elasticity theory of dislocation (Mansinha and Smylie, 1971)
Offshore: free transmission,
Landward: wave front (dry-wet) condition
Breakwater: Honma model, revetment:Aida modelNot considered

Tide level

Manning’s coefficient of roughness
Sea area: 0.03m-1/3·s, land area; 0.03m-1/3·s
T.P.±0.0m (T.P.: Tokyo peil)

Computation time interval

0.5s

Simulating time

4 hours after the occurrence of earthquake

Friction Coefficient(3) Computational region and grid size in FDM
Figure 6.1-1 shows the grid size of the computational region used in the numericalsimulation of tsunami. The grid size for the offing region is 1,350m, becoming more finely
divided closer to the coastal area so that it is 50m along the coastline.

Appendix 6- 2

Figure 6.1-1 Grid size of computational region in FDM

Appendix 6- 3

6.2. Configuration of standard fault model
According to the Headquarters for Earthquake Research Promotion (2004), earthquakes, which
occurred in the region ranging from Off Tokachi to Off Nemuro, may have been multi-segment
ruptures occurring at intervals between 400 and 500 years (500-year interval earthquakes), and thetime of the most recent occurrence was during the 17th century. Based on this, the focus in the sea
region ranging from the Kuril-Kamchatka Trench to the Japan Sea Trench is on a region that includes
the 500-year interval earthquakes off the coast of Hokkaido, which is considered to be the area where
the occurrence of a megathrust earthquake presents the greatest urgency.
The conditions for fault model were as follows.
[Configuration conditions]• Fault area: Junction with the Japan Trench to the Bussol Strait (assuming an earthquake
occurring along the boundary between the Kuril forearc sliver (DeMets, 1992) and Pacificplate)• Mean stress drop: Δσ=3(MPa)• Slip distribution: Large slip areas and very-large slip areas are set based on the approach set
forth in Cabinet Office (2012)
Table 6.2-1 shows the basic information of fault model for a M9-class megathrust earthquake
along the Kuril-Kamchatka Trench, as configured according to the aforementioned conditions.
Figure 6.2-1(1) shows the standard fault model. Also, Figures 6.2-1(2) through (5) show fault
models when large slip areas, which also include super large slip areas, move in accordance withpreviously described method for a simplified parametric study.

Appendix 6- 4

Table 6.2-1 Basic information of standard fault modelSpecification

ValuesLength (km)848

Area(×1,000km2)

159

Area ratio of the super large slip area and large slip area (%)

20.1

Average slip of whole area (m)10.0

Displacement of super large slip area (m)40.0

Displacement of large slip area (m)20.0

Displacement of background zone (m)

5.8

MW

9.2

Δσ (MPa)

3.0

Number of subfaults

1,961

Appendix 6- 5

Slip

Slip

(1) Centered large slip area (basic model)(2) Large slip area placed at the half point to east

Slip

Slip

(3) Large slip area placed at the eastern edge

(4) Large slip area placed at the half point to westSlip(5) Large slip area placed at the western edge
Figure 6.2-1 Standard fault model and trial fault models for simplified parametric study

Appendix 6- 6

6.3. Simplified parametric study
The simplified parametric study and detailed parametric study compared the analysis results withthe results of surveys of tsunami deposits (“run-up height records (deposits)”). The run-up heightrecords (deposits), which were used, were based on Hokkaido Government(2012), MEXT and
Hokkaido University (2010), MEXT and Hokkaido University (2011), and MEXT and Hokkaido
University (2012). Here, other than Hokkaido Government(2012), the position data were digitalized
from the reports as elevation values, so the values from the reports are treated as sample values.
Distribution of the run-up height records (deposits) is shown in Figure 6.3-1. Detailed data of
run-up height records (deposits) is also listed in Table 6.3-1.

Hamanaka-cho
Taiki-cho

Funka
Bay

Mori-machi-Washinoki

Figure 6.3-1 Distribution of run-up height records (tsunami deposits) (Hokkaido government, 2012)
Figure 6.3-2 shows a comparison of the run-up height records (deposits) and the calculation
results where the position of large slip area was moved. Here, in the vicinity of Nemuro City, when
the large slip area placed at the half point to west, calculated tsunami heights exceeded the run-up
height records (deposits). At most of the other trace points, when a large slip area was placed at“western edge”, the tsunami run-up height records (deposits) were either exceeded, or at the samelevel. Based on the aforementioned results, the detailed parametric study verified the effect ofAppendix 6- 7

uncertainty on the kinematic parameters of fault rupture by using models where large slip area wasplaced at “western edge”.
In Figure 6.3-2, all of the values calculated for trace points in the Hidaka region and Funka Bay
were lower than the tsunami run-up height records (deposits). As shown in Figure 6.3-3, it isconsidered that tsunami occurring along the Kuril-Kamchatka Trench (southern part) are obstructedby Cape Erimo and most large waves do not propagate in the Hidaka region or Funka Bay, which arelocated west of Cape Erimo.
Table 6.3-1 Detailed data of tsunami run-up height records (deposits)
No.
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40

TsunamiHeight (m)
15.0
4.0
10.0
10.0
15.5
1.0
5.0
12.0
8.0
5.0
12.0
4.0
7.0
8.0
12.0
7.0
10.0
12.0
15.0
10.0
15.0
18.0
11.0
12.0
17.0
9.0
10.0
12.0
5.0
5.0
7.0
5.0
4.5
5.0
2.3
15.5
4.9
4.9
4.7
1.4

Latitude LongitudePlace(deg.)(deg.)
43.34
145.72 Nemuro-shi
43.24
145.55 Nemuro-shi
43.24
145.55 Nemuro-shi
43.19
145.41 Nemuro-shi
43.19
145.41 Nemuro-shi
43.03
144.84 Hamanaka-cho
43.03
144.84 Hamanaka-cho
43.03
144.84 Hamanaka-cho
42.99
144.20 Kushiro-shi
42.92
144.00 Shiranuka-cho
42.92
144.00 Shiranuka-cho
42.88
143.92 Kushiro-shi-Onbetsu
42.88
143.92 Kushiro-shi-Onbetsu
42.88
143.92 Kushiro-shi-Onbetsu
42.83
143.84 Urahoro-cho
42.79
143.80 Urahoro-cho
42.76
143.76 Urahoro-cho
42.60
143.55 Toyokoro-cho
42.60
143.55 Toyokoro-cho
42.54
143.48 Taiki-cho
42.54
143.48 Taiki-cho
42.54
143.48 Taiki-cho
42.45
143.41 Taiki-cho
42.45
143.41 Taiki-cho
42.45
143.41 Taiki-cho
42.39
143.37 Hiroo-cho
42.39
143.37 Hiroo-cho
42.39
143.37 Hiroo-cho
42.33
142.38 Shin-Hidaka-cho
42.49
142.03 Hidaka-cho
42.57
141.91 Mukawa-cho
42.35
141.05 Cape Washibetsu
42.39
140.91 Date-shi-Kogane
42.12
140.54 Mori-machi-Washinoki
42.71
143.68 Urahoro-cho-Toyokita (sample)
43.19
145.41 Nemuro-shi-Bettoga (sample)
42.86
143.87 Nemuro-shi-Kinashibetsu (sample)
42.88
143.92 Nemuro-shi-Onbetsu (sample)
42.88
143.92 Nemuro-shi-Onbetsu (sample)
43.07
144.80 Akkeshi-cho-Shirahama (sample)

SourceHokkaido Government (2012)
Hokkaido Government (2012)
Hokkaido Government (2012)
Hokkaido Government (2012)
Hokkaido Government (2012)
Hokkaido Government (2012)
Hokkaido Government (2012)
Hokkaido Government (2012)
Hokkaido Government (2012)
Hokkaido Government (2012)
Hokkaido Government (2012)
Hokkaido Government (2012)
Hokkaido Government (2012)
Hokkaido Government (2012)
Hokkaido Government (2012)
Hokkaido Government (2012)
Hokkaido Government (2012)
Hokkaido Government (2012)
Hokkaido Government (2012)
Hokkaido Government (2012)
Hokkaido Government (2012)
Hokkaido Government (2012)
Hokkaido Government (2012)
Hokkaido Government (2012)
Hokkaido Government (2012)
Hokkaido Government (2012)
Hokkaido Government (2012)
Hokkaido Government (2012)
Hokkaido Government (2012)
Hokkaido Government (2012)
Hokkaido Government (2012)
Hokkaido Government (2012)
Hokkaido Government (2012)
Hokkaido Government (2012)
MEXT & Hokkaido University (2010-2012)
MEXT & Hokkaido University (2010-2012)
MEXT & Hokkaido University (2010-2012)
MEXT & Hokkaido University (2010-2012)
MEXT & Hokkaido University (2010-2012)
MEXT & Hokkaido University (2010-2012)

Note ) Tsunami heights of No.35-40 are sample only, since these are digitized altitude from the report

Appendix 6- 8

Tsunami height (m)area placed at the eastern edge

Appendix 6- 9

40Akkeshii‐cho‐Shirahama(sample)

39Kushiro‐shi‐Onbetsu(sample)

38Kushiro‐shi‐Onbetsu(sample)

37Kushiro‐shi‐Kinashibetsu(sample)

36Nemuro‐shi‐Bettoga(sample)

35Urahoro‐cho‐Toyokoro(sample)

34Mori‐machi‐Washinoki

33Date‐shi‐Kogane

32Cape Washibetsu

31Mukawa‐cho

30Hidaka‐cho

29Shin‐Hidaka‐cho

28Hiroo‐cho

27Hiroo‐cho

26Hiroo‐cho

25Taiki‐cho

24Taiki‐cho

23Taiki‐cho

22Taiki‐cho

21Taiki‐cho

20Taiki‐cho

19Toyokoro‐cho

18Toyokoro‐cho

17Urahoro‐cho

16Urahoro‐cho

15Urahoro‐cho

14Kushiro‐shi‐Onbetsu

13Kushiro‐shi‐Onbetsu

12Kushiro‐shi‐Onbetsu

11Shiranuka‐cho

10Shiranuka‐cho

09Kushiro‐shi

08Hamanaka‐cho

07Hamanaka‐cho

06Hamanaka‐cho

05Nemuro‐shi

04Nemuro‐shi

03Nemuro‐shi

02Nemuro‐shi

01Nemuro‐shi

20
18
16
14
12
10
8
6
4
2
0
Tsunami trace

Cal. (basic model)

Cal. (half‐east)

Cal. (eastern edge)

Cal. (half‐west)

Cal. (western edge)

Figure 6.3-2 Comparison of the calculated tsunami heights obtained from the parametric study withrespect to the location of large slip area and the tsunami run-up height records(deposits)

W.L.(m)Cape Erimo

Figure 6.3-3 Distribution map of maximum water level in the calculation case in which large slip

6.4. Detailed parametric study
The detailed parametric study examined the uncertainty of kinematic parameters for fault rupture.
Based on the results of the simplified parametric study, it was decided to use a “model where alarge slip area was placed at the western edge” for the fault model in the study.
(1) Effect of hypocenter and rupture velocity on tsunami height
The positions of hypocenters are as shown in Figure 6.4-1, and there were five points aroundlarge slip areas and one point in the center of a super large slip area. Also, four cases were set for
rupture velocity: Vr: Vr=1.0(km/s), Vr=2.0(km/s), Vr=2.5(km/s), and Vr=3.0(km/s). Figure 6.4-2
shows an example of a rupture propagation time distribution for a fault in keeping with the rupture
velocities in the case of hypocenter (d).

(a)
(c)
(b)

(e)
(f)

(d)

Slip

Figure 6.4-1 Location of the hypocenters (Large slip area placed at the eastern edge)

Appendix 6- 10

Hypocenter (d), Vr=1.0km

Hypocenter (d), Vr=2.0km

Rupture propagation time (s)Rupture propagation time (s)(1) Vr=1.0(km/s)(2) Vr=2.0(km/s)

Hypocenter (d), Vr=2.5km

Hypocenter (d), Vr=3.0km

Rupture propagation time (s)(3) Vr=2.5(km/s)

Rupture propagation time (s)(4) Vr=3.0(km/s)

Figure 6.4-2 Distribution of rupture propagation time in the case of hypocenter (d) (Large slip area
placed at the eastern edge)

Appendix 6- 11

Figure 6.4-3 shows the results of parametric studies of hypocenters and rupture velocities.
It was found that, over a range extending from Kushiro City to Hiroo Town which is located in
front of a large slip area, the tsunami height level varied significantly due to the effects of locationof hypocenter and rupture velocity.
Figure 6.4-4 shows a comparison of the maximum water levels from the parametric study
results with the tsunami run-up height records (deposits). Figure 6.4-4(1) shows a comparison of
the maximum water levels from the detailed parametric study with the tsunami run-up heightrecords (deposits), and Figure 6.4-4(2) shows the maximum water levels from all parametricstudies, which is a combination of the simplified parametric study and detailed parametric study,
with the tsunami run-up height records (deposits). At most of the run-up height records (deposits)with the exception of the area ranging from the Hidaka region to Funka Bay, the result was thatthe maximum envelope of the calculated values exceeded the tsunami run-up height records(deposits).
Of the sites where surveys were conducted for tsunami trace values (tsunami deposits), three
representative sites (Hamanaka-cho, Taiki-cho, and Mori–machi-Washinoki) were targeted toverify the effect that location of rupture initiation pointhypocenter and rupture - velocity have ontsunami height. The results are given in Figure 6.4-5. A trend was observed where tsunami heightincreased in cases where the rupture initiated from a location close to the trench axis ((b), (d) and(f)). With regard to the effect of rupture velocity, the trend differed depending upon the locationof the rupture initiation pointhypocenter, and, in cases where the rupture initiated in the vicinityof the trench axis ((b), (d) and (f)), a trend was observed where the tsunami height would be larger
the smaller the rupture velocity was. On the other hand, in cases where the rupture initiated along
the coast ((a), (c) and (e)), the opposite trend was observed.

Appendix 6- 12

Tsunami height (m)
20
18
16
14
12
10
8
6
4
2
0

Appendix 6- 13
40Akkeshii‐cho‐…

39Kushiro‐shi‐Onbetsu(sample)

38Kushiro‐shi‐Onbetsu(sample)

37Kushiro‐shi‐…

36Nemuro‐shi‐Bettoga(sample)

35Urahoro‐cho‐…

34Mori‐machi‐Washinoki

33Date‐shi‐Kogane

32Cape Washibetsu

31Mukawa‐cho

30Hidaka‐cho

29Shin‐Hidaka‐cho

28Hiroo‐cho

27Hiroo‐cho

26Hiroo‐cho

25Taiki‐cho

24Taiki‐cho

23Taiki‐cho

22Taiki‐cho

21Taiki‐cho

20Taiki‐cho

19Toyokoro‐cho

18Toyokoro‐cho

17Urahoro‐cho

16Urahoro‐cho

15Urahoro‐cho

14Kushiro‐shi‐Onbetsu

13Kushiro‐shi‐Onbetsu

12Kushiro‐shi‐Onbetsu

11Shiranuka‐cho

10Shiranuka‐cho

09Kushiro‐shi

08Hamanaka‐cho

07Hamanaka‐cho

06Hamanaka‐cho

05Nemuro‐shi

04Nemuro‐shi

03Nemuro‐shi

02Nemuro‐shi

01Nemuro‐shi

Tsunami height (m)40Akkeshii‐cho‐…

39Kushiro‐shi‐Onbetsu(sample)

38Kushiro‐shi‐Onbetsu(sample)

37Kushiro‐shi‐…

36Nemuro‐shi‐Bettoga(sample)

35Urahoro‐cho‐…

34Mori‐machi‐Washinoki

33Date‐shi‐Kogane

32Cape Washibetsu

31Mukawa‐cho

30Hidaka‐cho

29Shin‐Hidaka‐cho

28Hiroo‐cho

27Hiroo‐cho

26Hiroo‐cho

25Taiki‐cho

24Taiki‐cho

23Taiki‐cho

22Taiki‐cho

21Taiki‐cho

20Taiki‐cho

19Toyokoro‐cho

18Toyokoro‐cho

17Urahoro‐cho

16Urahoro‐cho

15Urahoro‐cho

14Kushiro‐shi‐Onbetsu

13Kushiro‐shi‐Onbetsu

12Kushiro‐shi‐Onbetsu

11Shiranuka‐cho

10Shiranuka‐cho

09Kushiro‐shi

08Hamanaka‐cho

07Hamanaka‐cho

06Hamanaka‐cho

05Nemuro‐shi

04Nemuro‐shi

03Nemuro‐shi

02Nemuro‐shi

01Nemuro‐shi

20
18
16
14
12
10
8
6
4
2
0
Tsunami trace

Vr=∞(a)，Vr=1.0km/s(a)，Vr=2.0km/s(a)，Vr=2.5km/s(a)，Vr=3.0km/s(b)，Vr=1.0km/s(b)，Vr=2.0km/s(b)，Vr=2.5km/s(b)，Vr=3.0km/s(c)，Vr=1.0km/s(c)，Vr=2.0km/s(c)，Vr=2.5km/s(c)，Vr=3.0km/s(1) Results in the case of hypocenter (a) ~ (c)Tsunami trace

Vr=∞(d)，Vr=1.0km/s(d)，Vr=2.0km/s(d)，Vr=2.5km/s(d)，Vr=3.0km/s(e)，Vr=1.0km/s(e)，Vr=2.0km/s(e)，Vr=2.5km/s(e)，Vr=3.0km/s(f)，Vr=1.0km/s(f)，Vr=2.0km/s(f)，Vr=2.5km/s(f)，Vr=3.0km/s(2) Results in the case of hypocenter (d) ~ (f)Figure 6.4-3 Results of parametric studies with respect to the hypocenter and the rupture velocity

Tsunami height (m)
20
18
16
14
12
10
8
6
4
2
0

tsunami run-up height records (deposits)

Appendix 6- 14
40Akkeshii‐cho‐…

39Kushiro‐shi‐Onbetsu(sample)

38Kushiro‐shi‐Onbetsu(sample)

37Kushiro‐shi‐…

36Nemuro‐shi‐Bettoga(sample)

35Urahoro‐cho‐…

34Mori‐machi‐Washinoki

33Date‐shi‐Kogane

32Cape Washibetsu

31Mukawa‐cho

30Hidaka‐cho

29Shin‐Hidaka‐cho

28Hiroo‐cho

27Hiroo‐cho

26Hiroo‐cho

25Taiki‐cho

24Taiki‐cho

23Taiki‐cho

22Taiki‐cho

21Taiki‐cho

20Taiki‐cho

19Toyokoro‐cho

18Toyokoro‐cho

17Urahoro‐cho

16Urahoro‐cho

15Urahoro‐cho

14Kushiro‐shi‐Onbetsu

13Kushiro‐shi‐Onbetsu

12Kushiro‐shi‐Onbetsu

11Shiranuka‐cho

10Shiranuka‐cho

09Kushiro‐shi

08Hamanaka‐cho

07Hamanaka‐cho

06Hamanaka‐cho

05Nemuro‐shi

04Nemuro‐shi

03Nemuro‐shi

02Nemuro‐shi

01Nemuro‐shi

Tsunami height (m)01Nemuro‐shi
02Nemuro‐shi
03Nemuro‐shi
04Nemuro‐shi
05Nemuro‐shi
06Hamanaka‐cho
07Hamanaka‐cho
08Hamanaka‐cho
09Kushiro‐shi
10Shiranuka‐cho
11Shiranuka‐cho
12Kushiro‐shi‐Onbetsu
13Kushiro‐shi‐Onbetsu
14Kushiro‐shi‐Onbetsu
15Urahoro‐cho
16Urahoro‐cho
17Urahoro‐cho
18Toyokoro‐cho
19Toyokoro‐cho
20Taiki‐cho
21Taiki‐cho
22Taiki‐cho
23Taiki‐cho
24Taiki‐cho
25Taiki‐cho
26Hiroo‐cho
27Hiroo‐cho
28Hiroo‐cho
29Shin‐Hidaka‐cho
30Hidaka‐cho
31Mukawa‐cho
32Cape Washibetsu
33Date‐shi‐Kogane
34Mori‐machi‐Washinoki
35Urahoro‐cho‐…
36Nemuro‐shi‐Bettoga(sample)
37Kushiro‐shi‐…
38Kushiro‐shi‐Onbetsu(sample)
39Kushiro‐shi‐Onbetsu(sample)
40Akkeshii‐cho‐…

20
18
16
14
12
10
8
6
4
2
0
Tsunami trace

Vr=∞

Detailed parametric study((a)‐(f))(1) Results of detailed parametric study

Tsunami trace

Vr=∞

Max. of whole parametric studies(2) Results of whole parametric study (simplified and detailed)Figure 6.4-4 Comparison of calculated tsunami heights obtained from the parametric study and the07 Hamanaka‐cho

07 Hamanaka‐cho
6.0

Vr=∞
(a)

Tsunami height (m)Tsunami height (m)

6.0

(b)
(c)

5.0

(d)
(e)

trench axis side

Vr=∞
Vr=1.0km/s
Vr=2.0km/s
Vr=2.5km/s

5.0

Vr=3.0km/s

(f)
4.0

4.0
1.0

1.5

2.0

2.5

3.0

(a)

Rupture velocity (km/s)(b)(d) (e)(f)(2) Effect of location of hypocenter on tsunami height inHamanaka-cho(1) Effect of rupture velocity on tsunami height inHamanaka-cho
21 Taiki‐cho

21 Taiki‐cho

20.0

20.0

Vr=∞
(a)
(b)
(c)

15.0

(d)
(e)

Tsunami height (m)Tsunami height (m)(c)

Rupture initiation point

trench axis side

Vr=∞
Vr=1.0km/s
Vr=2.0km/s
Vr=2.5km/s

15.0

Vr=3.0km/s

(f)
10.0

10.0
1.0

1.5

2.0

2.5

3.0

(a) (b) (c) (d) (e) (f)Rupture velocity (km/s)

Rupture initiation point(3) Effect of rupture velocity on tsunami height in Taiki- (4) Effect of location of hypocenter on tsunami height inchoTaiki-cho
34 Mori‐machi‐Washinoki

34 Mori‐machi‐Washinoki
3.0

Vr=∞
(a)
(b)
(c)

2.0

(d)
(e)

Tsunami height (m)Tsunami height (m)3.0

trench axis side

Vr=∞
Vr=1.0km/s
Vr=2.0km/s
Vr=2.5km/s

2.0

Vr=3.0km/s

(f)
1.0

1.0
1.0

1.5

2.0

2.5

3.0

(a)

Rupture velocity (km/s)(b)(c) (d) (e)(f)

Rupture initiation point(5) Effect of rupture velocity on tsunami height in
Mori-machi-Washinoki(6) Effect of location of hypocenter on tsunami height in
Mori-machi-Washinoki

Figure 6.4-5 Effect of hypocenter and rupture velocity on tsunami heights

Appendix 6- 15

(2) Effect of rise time on tsunami height
A parametric study of rise time was conducted. Here, four scenarios were examined setting
the rise time at 30 seconds, 60 seconds, 180 seconds, and 300 seconds, and two cases were
examined: a case where rupture velocity was not considered (Vr=∞) and a case where rupture
velocity was set at Vr=2.5(km/s) with the hypocenter (b).
Figure 6.4-6 shows the results of the case where rupture velocity was not considered (Vr=∞).
Figure 6.4-7 shows the results of a case where the rupture velocity was set at Vr=2.5(km/s) andthe hypocenter was (b). Based on a comparison of the results, a trend was observed with respect
to the effect of rise time where the tsunami height decreased the longer the rise time was. However,
the effect on tsunami height was not very pronounced within a range where the rise time was not

20
18
16
14
12
10
8
6
4
2
0

Tsunami trace
30 s
60 s
180 s

4.0

12.0

10.0

8.0
0

100

200

Rise time (s)300

39Kushiro‐shi‐Onbetsu(sample)

40Akkeshii‐cho‐Shirahama(sample)

38Kushiro‐shi‐Onbetsu(sample)

36Nemuro‐shi‐Bettoga(sample)

37Kushiro‐shi‐Kinashibetsu(sample)

35Urahoro‐cho‐Toyokoro(sample)

33Date‐shi‐Kogane

1.8
Tsunami height (m)Tsunami height (m)4.534Mori‐machi‐Washinoki

34 Mori‐machi‐Washinoki（Vr=∞）

14.0

5.0

32Cape Washibetsu

30Hidaka‐cho

31Mukawa‐cho

28Hiroo‐cho

29Shin‐Hidaka‐cho

27Hiroo‐cho

25Taiki‐cho

26Hiroo‐cho

24Taiki‐cho

23Taiki‐cho

22Taiki‐cho

21Taiki‐cho

20Taiki‐cho

21 Taiki‐cho（Vr=∞）

5.5
Tsunami height (m)19Toyokoro‐cho

17Urahoro‐cho

07 Hamanaka‐cho（Vr=∞）

18Toyokoro‐cho

15Urahoro‐cho

16Urahoro‐cho

14Kushiro‐shi‐Onbetsu

13Kushiro‐shi‐Onbetsu

11Shiranuka‐cho

12Kushiro‐shi‐Onbetsu

09Kushiro‐shi

10Shiranuka‐cho

08Hamanaka‐cho

07Hamanaka‐cho

05Nemuro‐shi

06Hamanaka‐cho

04Nemuro‐shi

03Nemuro‐shi

02Nemuro‐shi

300 s

01Nemuro‐shi

Tsunami height (m)extremely long (30 ~ 60 seconds).

1.6

1.4

1.2
0

100

200

300

0

Rise time (s)Figure 6.4-6 Effects of rise time on tsunami heights (Vr=∞)

Appendix 6- 16

100

200

Rise time (s)300Tsunami height (m)
5.0

4.5

Tsunami height (m)5.5

07 Hamanaka‐cho（(b), Vr=2.5km/s）

4.0
0
100
200

Rise time (s)
300
14.0

12.0

Tsunami height (m)Tsunami height (m)

0
100
200

Rise time (s)Appendix 6- 17

10.0
300

16.0

21 Taiki‐cho（(b), Vr=2.5km/s）

0100

40Akkeshii‐cho‐Shirahama(sample)

39Kushiro‐shi‐Onbetsu(sample)

38Kushiro‐shi‐Onbetsu(sample)

37Kushiro‐shi‐Kinashibetsu(sample)

36Nemuro‐shi‐Bettoga(sample)

35Urahoro‐cho‐Toyokoro(sample)

34Mori‐machi‐Washinoki

33Date‐shi‐Kogane

32Cape Washibetsu

31Mukawa‐cho

30Hidaka‐cho

29Shin‐Hidaka‐cho

28Hiroo‐cho

27Hiroo‐cho

26Hiroo‐cho

25Taiki‐cho

24Taiki‐cho

23Taiki‐cho

22Taiki‐cho

21Taiki‐cho

20Taiki‐cho

19Toyokoro‐cho

18Toyokoro‐cho

17Urahoro‐cho

16Urahoro‐cho

15Urahoro‐cho

14Kushiro‐shi‐Onbetsu

13Kushiro‐shi‐Onbetsu

12Kushiro‐shi‐Onbetsu

11Shiranuka‐cho

10Shiranuka‐cho

09Kushiro‐shi

08Hamanaka‐cho

07Hamanaka‐cho

06Hamanaka‐cho

05Nemuro‐shi

04Nemuro‐shi

03Nemuro‐shi

02Nemuro‐shi

01Nemuro‐shi

20
18
16
14
12
10
8
6
4
2
0
Tsunami trace

30 s

60 s

Rise time (s)200

Figure 6.4-7 Effects of rise time on tsunami heights (hypocenter (b), Vr=2.5km/s)
180 s

300 s

2.0

34 Mormachi（(b), Vr=2.5km/s）

1.8

1.6

1.4
300

6.5. Summary
The findings that was obtained from an examination of deterministic tsunami hazard analysis,
which focused on the sea area extending from the Kuril-Kamchatka Trench to the Japan Sea Trench,
is summarized below.
• For a region that includes the source region of the 500-year interval earthquakes in the Off
Hokkaido, a standard fault model (MW9.2), which was based upon the approach presented by
Cabinet Office (2012), was considered and a deterministic hazard analysis was conducted.
• The results of simplified and detailed parametric studies showed that the maximum envelope ofthe calculated values exceeded tsunami run-up height records (tsunami deposits) at most of thetsunami trace points with the exception of the area ranging from the Hidaka region to Funka Bay.
• A detailed parametric study was conducted in order to verify the effects of kinematic parametersof fault rupture (hypocenter, rupture velocity, and rise time) on tsunami heights along thecoastline.
- In an area of open coastline that front large slip areas (comparison point: Taiki-cho), it was
found that, while kinematic parameters act greatly on tsunami height, the tsunami height is noteasily affected by these within a harbor (comparison points: Mori–machi-Washinoki and
Hamanaka-cho).
- With regard to the effect that location of hypocenter has on tsunami height along the coastline,
a trend was observed where tsunami height increased when rupture initiated at locations close
to the trench axis.
- With regard to the effect of rupture velocity, a trend was observed where the tsunami height
would be larger the smaller the rupture velocity was in cases where the rupture initiated in thevicinity of a trench axis.
- With regard to the effect of rise time, a trend was observed where the tsunami height decreased
the longer the rise time was. However, the effect on tsunami height was not very pronounced
within a range where the rise time was not extremely long (30 ~ 60 seconds).

[Appendix 6 References]
Committee for Evaluating the Rupture Model of Megathrust Earthquakes along the Nankai Troughunder Cabinet Office, Government of Japan (2012): The 2nd Report of Committee for
Evaluating the Rupture Model of Megathrust Earthquakes along the Nankai Trough: Tsunami
Fault Model Version -Tsunami Fault Model, Tsunami Height, Tsunami Flooded Area and etc.(in Japanese).
Appendix 6- 18http://www.bousai.go.jp/jishin/nankai/model/pdf/20120829_2nd_report01.pdf (Accessed on
August 2014).
DeMets, C. (1992): Oblique Convergence and Deformation Along the Kuril and Japan Trenches,
Journal of Geophysical Research, Vol. 97, No. B12, pp. 17615-17625.
Headquarters for Earthquake Research Promotion (2004): Long-term Evaluations of seismic activities
along the Kuril Trench (2nd edition), pp. 1-81 (in Japanese).
Hokkaido Government (2012): Report on the Development of Hazard Maps of Tsunami Inundation
along the Pacific Coast of Hokkaido, Japan (in Japanese).
Mansinha, L. and D. E. Smylie (1971): The displacement fields of inclined faults, Bulletin of the
Seismological Society of America, Vol. 61, No. 5, pp. 1433-1440.
MEXT (Ministry of Education, Culture, Sports, Science and Technology, Japan) and Hokkaido
University (2010): Annual Report 2009 on the Investigation and Research into the Off Nemuro
Earthquakes, Japan (in Japanese).
MEXT (Ministry of Education, Culture, Sports, Science and Technology, Japan) and Hokkaido
University (2011): Annual Report 2010 on the Investigation and Research into the Off Nemuro
Earthquakes, Japan (in Japanese).
MEXT (Ministry of Education, Culture, Sports, Science and Technology, Japan) and Hokkaido
University (2012): Annual Report 2011 on the Investigation and Research into the Off Nemuro
Earthquakes, Japan (in Japanese).
Seto, S. and T. Takahashi (2014): Recipe of Predicting Multi Tsunami Scenarios in the Nankai Troughand Its Application, Journal of JSCE, B2 (Coastal Engineering), Vol. 70, No. 2, pp. I_351I_355 (in Japanese).
Shuto, N. and M. Uhana (1984): Height of the 1983 Japan Sea Earthquake-Tsunami, Research Reportof Tsunami Disaster Prevention Laboratory, School of Engineering, Tohoku University, Vol. 1(in Japanese).

Appendix 6- 19

Chapter 7. Examples of Applications of ProbabilisticTsunami Hazard Analysis“Notes: Examples of Applications of Probabilistic Tsunami Hazard Analysis”
The examples of applications of probabilistic tsunami hazard analysis, which are presented inthis chapter, are premised on logic tree assumptions, earthquake occurrence frequency, magnitude
and other characteristics given as conditions, and illustrate the procedures and results of the logic
tree construction, modeling earthquake occurrence, and other matters presented in Chapter 5 of themain volume.
In accordance with the aforementioned purpose, it should be kept in mind that these application
examples are neither limitations on earthquake occurrence frequency, magnitude or othercharacteristics nor do they negate other methods that take into consideration uncertainty. Also, theconfiguration of logic trees and other elements presented in these application examples are entirely
illustrative. In actual probabilistic tsunami hazard analyses, sufficient consideration needs to begiven to the appropriateness of logic trees and other analysis elements.

An example of a probabilistic tsunami hazard analysis for the sea region extending from theKuril Trench to the Japan Trench is presented. Just as in with the assessment by Japan Society of
Civil Engineers (2011), the target sites were Fudai Village and Yamada Town in Iwate Prefecture.
7.1. Logic tree construction(1) Source region and occurrence patternFigure 7.1-1 shows the source regions. This analysis examines the multi-segment rupture
type earthquakes ((a), (b), (c) and (d)), tsunami earthquakes (JTT), and normal fault earthquakes
within the oceanic plate (JTNR).
With regard to the multi-segment rupture type earthquake models, branches were configured
as to whether they are considered as the characteristic earthquake model identifying the region or
the G-R model which does not identify the region. In addition, in case of the characteristic
earthquake model, inter-regional multi-segment ruptures were also taken into account andconfigured as branches ((a)+(b), (b)+(c) and (a)+(b)+(c)). With regard to the position of large sliparea in (c), branches were configured for those “anywhere” which varies within the region, andthose “fixed” which is the same position as the 2011 Tohoku earthquake, each time.

Appendix 7 - 1

(2) Magnitude distribution (distribution of mean stress drop)
With regard to the multi-segment rupture type earthquakes ((a)~(d)), In the case of thecharacteristic earthquake model, magnitude distribution was computed based upon mean stressdrop and region area. Also, in the G-R model, based upon MW computed from the area of eachregion where mean stress drop was 3MPa ((a): MW8.8, (b): MW8.7, (c): MW9.0, and (d): MW8.7),
three branches were set for the magnitude range: up to MW for (c) (MW8.7~9.0), up to MW for(b)+(c) (MW8.7~9.2), and up to MW for (a)+(b)+(c) (MW8.7~9.3).
The largest historical MW was taken into account for tsunami earthquakes (JTT) and normal
fault earthquakes within the oceanic plate (JTNR) in configuring the magnitude distribution.
(3) Fault models
With regard to the multi-segment rupture type earthquakes ((a)~(d)), the characterizedtsunami source model was used that configured large slip area and super large slip area based
upon the approach presented in Cabinet Office (2012a). However, for the branch for “fixed in the
Miyagi Prefecture offing” for (c), a model was used that reproduced the 2011 Tohoku earthquake
according to Cabinet Office (2012b). A fault model, which was the same as that in Japan Societyof Civil Engineers (2011), was used for the tsunami earthquakes (JTT) and normal fault
earthquakes within the oceanic plate (JTNR).
(4) Mean recurrence interval• Tokachi-oki to Nemuro-oki: region (a)A frequency of one in six times for a multi-segment rupture in the area of the Tokachi-oki
and the Nemuro-oki (the Japan Society of Civil Engineers, 2011), and a mean recurrence intervalof 72.2 years for the area of the Tokachi-oki and the Nemuro-oki as postulated by the
Headquarters for Earthquake Research Promotion (2004) were taken into consideration to set themean recurrence interval at 430 years. Moreover, branches were configured for the possibility
and the frequency of including tsunami earthquake regions.
• Northern Sanriku-oki: region (b)The mean recurrence interval of interplate earthquakes in the northern area of Sanriku-oki
was set at 97 years based upon the history of the past four occurrences (in 1677, 1763, 1856, and1968), and the frequency of including tsunami earthquake regions was postulated so that it would
be the same as the mean recurrence interval of (c).
• Central Sanriku-oki to Ibaraki Prefecture-oki: region (c)A mean recurrence interval of 600 years was applied, which was for the past fiveearthquakes postulated by the Headquarters for Earthquake Research Promotion (2011).
Branches for the frequency of including tsunami earthquake regions were configured on the
Appendix 7 - 2

assumption that multi-segment ruptures, in four occurrences other than in 2011 out of the recordsof the past five occurrences, might occur four, one, and zero times.
• Ibaraki Prefecture-oki to Boso-oki: region (d)The mean recurrence interval was set at the same as that for (c) as well as one-third of thislevel.
• Inter-regional multi-segment ruptures: (a)+(b), (b)+(c) and (a)+(b)+(c)It was assumed that inter-regional multi-segment ruptures would occur one every three times
each earthquake would occur. The mean recurrence interval for (a)+(b) was set based on the mean
recurrence interval for (a), the mean recurrence interval for (b)+(c) was set based on the mean
recurrence interval for (c), and the mean recurrence interval for (a)+(b)+(c) was set on theassumption that it would occur one in every three times that an inter-regional multi-segment
rupture occurred for segments (b)+(c).
• Tsunami earthquakes: JTT
Although the Headquarters for Earthquake Research Promotion (2011) stated that tsunami
earthquakes (JTT) have occurred four times in a period of 412 years (in 1611, 1677, 1896, and2011), there is also the point of view that the 1611 tsunami was caused by a normal fault
earthquake within the oceanic plate, so a branch was configured for the 1611 tsunami. For the
branch where the 1611 tsunami caused by “the normal fault earthquake”, a mean recurrence
interval of 100 years was set based upon the four occurrences during a period of 412 years, anda branch was configured from the section for reliability of Poisson variables. For the branch where
the 1611 tsunami caused by “the tsunami earthquake”, it was configured as three occurrences
during a period of 412 years.
• Normal fault earthquakes within oceanic plates: JTNR
The Headquarters for Earthquake Research Promotion (2011) stated that there was one
normal fault earthquake within the oceanic plate (JTNR) that occurred during a period of 412
years. For the branch where the “1611 tsunami caused by a tsunami earthquake”, a mean
recurrence interval of 410 years was set based upon one occurrence during a period of 412 years,
and a branch was configured from the confidence interval of Poisson variables. For the branchwhere the ng a period of 412 years, normal earthquake, variables. For the branch where theoccurrences during a period of 412 years.
• G-R model
As shown in Table 7.1-1, the number of M7.9 or greater earthquakes along the Japan Trench
has been computed to be six with the exception of tsunami earthquakes during the period of 412
years since 1600. As shown in Figure 7.1-2, when the b value in the modified G-R equation is
0.9 and the maximum magnitude M9.3, the mean frequency is estimated to be 0.002224 = 1/450(year) for M8.7 or greater.
Appendix 7 - 3

(5) Error standard deviation and truncation threshold
For the error standard deviation and truncation threshold, in addition to a branch based onJapan Society of Civil Engineers (2011) (κ=1.25~1.55, truncation 2.3β, 10β), a branch was
configured based on the results of the examination described in Appendix volume 5.1 (κ=1.3, 1.4,
truncation 3β).
(6) Logic trees and branch weights
Figures 7.1-3 through 7.1-15 show the logic trees constructed based upon the
aforementioned approach. Branch weights were configured based upon Table 5.2.4-1 in the main
volume and the 7.1-3 through 7.1-15 show the logic trees constructed based upon the
aforementioned approach.

Appendix 7 - 4

KT2
KT1

(a)
KTR1

(b)

Fudai Village

JTN1

JTN3

Yamada Town
JTN2

(c)

JTS2

JTS1

(d)

JTT

JTNR

Themulti-segment rupture type earthquakes
 (a) Tokachi-oki to Nemuro-oki
 (b) Northern Sanriku-oki (c) Central Sanriku-oki to Ibaraki
Prefecture-oki (d) Ibaraki Prefecture-oki to Boso-oki
Tsunami earthquakes
 JTT
Intraplate earthquakes
 JTNR

Figure 7.1-1 The target points and tsunami source regions

Appendix 7 - 5

Table 7.1-1 Interplate earthquakes which occur in 412 years from 1600 to 2011(except tsunami
earthquakes) (The Headquarters for Earthquake Research Promotion, 2011)No.

Earthquake area

Occurrence date

Earthquake scale(M)1Northern Sanriku-oki

1677/4/13

73/4 ~ 8.0

2

Northern Sanriku-oki

1763/1/29

7.9

3Northern Sanriku-oki

1856/8/23

7.8 ~ 8.0

4Northern Sanriku-oki

1968/5/16

8.3 (MW)

1793/2/17

7.9

2011/3/11

9.0 (MW)5
6Southern Sanriku-oki
closer trench
Tohoku-oki

Figure 7.1-2 The results that applied modified G-R equation upper limit M9.3 to interpolate
earthquakes along Japan trench

Appendix 7 - 6

The model of multi-segment

Long-term: 0.70
Instantaneous: 1.00

Characteristic modelMulti-segment(Characteristic)

G-R model

Multi-segment
（G-R）

JTT
Long-term: 0.30
Instantaneous: 0.00

JTNR

Figure 7.1-3 The basic structure of logic tree for all tsunami sources

The probability ofinter-regional multi-segment
0.50

The classification of area(a), (b) and (c) haveno interaction

(a)

(b)

(c)

0.40

(a) and (b) are
interconnective

(a)

(b)

(c)

(d)

(a) + (b)0.40(b) and (c) are
interconnective

(a)

(b)

(c)

(d)

(b) + (c)0.20(a), (b) and (c) are
interconnective

(a)

(b)

(c)

(d)

(a) + (b)No

Multi-segment(Characteristic)
0.50

Exist

Tsunami source area(b) + (c)(a) + (b) + (c)Figure 7.1-4 The logic tree of characteristic earthquake model (branches regarding inter-regional
multi-segment rupture type earthquakes)

The probability ofincluding tsunami earthquake

Fault model

The range ofstress drop

The frequency ofincluding tsunami earthquake
1/3

0.50
0.50

Exist

Characteristic

0.50

0.50

Every time

430 years

Once in 3 times

1200 years

Once in 5 times

2100years

The frequency ofincluding tsunami earthquake

Occurrence interval

0.82 to 3.00 MPa

1/3

1.14 to 2.17 MPa

1/3

(a)

Occurrence interval

No

Figure 7.1-5 The logic tree of region (a)The probability ofincluding tsunami earthquake

Fault model

The range ofstress drop

1/3
0.50
0.50

Exist

Characteristic

0.50

0.82 to 3.00 MPa

1/3

1.14 to 2.17 MPa

1/3

(b)
0.50

No

Figure 7.1-6 The logic tree of region (b)Appendix 7 - 7

Once in 6 times

580 years

Once in 18 times

1700 years

Once in 30 times

2900 years

The position of asperity

Fault model

The range ofStress drop

The frequency of
Including tsunami earthquake
1/3

0.50

(c)

0.50

Fixed

Cabinet Office

Anywhere

Characteristic

1.00

Every time

600 years

Once in 3 times

1800 years

Once in 5 times

3000 years

The frequency ofincluding tsunami earthquake

Occurrence interval

0.82 to 3.00 MPa

1/3

1.14t o2.17 MPa

1/3

0.00

Occurrence interval

Figure 7.1-7 The logic tree of region (c)The probability ofincluding tsunami earthquake

Fault model

The range ofstress drop

0.10
1/3

0.50
0.50

Exist

Characteristic

0.50

0.82 to 3.00 MPa

Every time

0.90

0.10
1/3

Once in 3 times

1.14 to 2.17 MPa

0.90

0.10
1/3

(d)

0.50

Once in 5 times

0.90

No

Figure 7.1-8 The logic tree of region (d)Fault model

The range ofstress drop

Occurrence interval of (a)

1/3
0.50

(a) + (b)Characteristic

0.50

0.82 to 3.00 MPa

1/3

1.14 to 2.17 MPa

1/3

430 years

1200 years

1200 years

3600 years

2100 years

6300 years

Figure 7.1-9 The logic tree of (a)+(b)Appendix 7 - 8

Occurrence interval

200 years
600 years
600 years
1800 years
1000 years
3000 years

Fault model

The range ofstress drop amountOccurrence interval of (c)

1/3
0.50

(b) + (c)Characteristic

0.50

0.82 to 3.00 MPa

1/3

1.14 to 2.17 MPa

1/3

Occurrence interval

600 years

1800 years

1800 years

5400 years

3000 years

9000 years

Figure 7.1-10 The logic tree of (b)+(c)Fault model

The range ofstress drop amountOccurrence interval of (b) + (c)

1/3
0.50

(a) + (b) + (c)Characteristic

0.50

0.82 to 3.00 MPa

1/3

1.14 to 2.17 MPa

1/3

Occurrence interval

1800 years

5400 years

5400 years

16200 years

9000 years

27000 years

Figure 7.1-11 The logic tree of (a)+(b)+(c)Fault model

Magnitude range

Cause of1611 tsunami

Occurrence interval

0.25
0.35
0.15

JTT

Uniform model
1896 type[0.5]1677 type[0.5]

0.25
0.10
0.15

MC =8.3, BM=0.5

0.70

MC =8.3, BM=0.3

The tsunami
earthquake

0.25

MC =8.2, BM=0.5
MC =8.2, BM=0.3
MC =8.1, BM=0.5

0.25
0.30

The normal fault
earthquake

Figure 7.1-12 The logic tree of JTT

Appendix 7 - 9

0.50

0.50
0.25

57 years
100 years
190 years
69 years
130 years
300 years

Fault modelOccurrence pattern

Magnitude range

0.25
0.25
0.05

Only position
occurred in the past

0.30
0.10
0.10

0.30
0.20

JTNR

Uniform model

0.05

Anywhere in
northern area

0.30
0.10
0.10

0.35
0.20

0.90

Anywhere in
active area

0.25
0.10
0.10

Cause of1611 tsunami

MC =8.4, BM=0.5
MC =8.4, BM=0.3
MC =8.3, BM=0.5
MC =8.3, BM=0.3
MC =8.2, BM=0.5
MC =8.4, BM=0.5

0.25
0.70

MC =8.4, BM=0.3

The tsunami
earthquake

MC =8.3, BM=0.5
MC =8.3, BM=0.3

0.70

Multi-segment（G-R）

Characteristic

0.20
0.10

0.25
0.30

MC =8.2, BM=0.5

The normal fault
earthquake

MC =8.4, BM=0.3
MC =8.3, BM=0.5
MC =8.3, BM=0.3
MC =8.2, BM=0.5

Magnitude range

Occurrence interval

Mw 8.7 to 9.0

450 years

Mw 8.7 to 9.2

450 years

Mw 8.7 to 9.3

450 years

Figure 7.1-14 The logic tree of G-R model

0.50
0.25

MC =8.4, BM=0.5

Appendix 7 - 10

0.50
0.25

Figure 7.1-13 The logic tree of normal fault earthquakes within oceanic plate (JTNR)

Fault modelOccurrence interval

120 years
410 years
2300 years
89 years
200 years
580 years

Error standard deviation and truncation threshold

0.50

0.50

Based on Japan Society of
Civil Engineers (2011)

Based on the study after the2011 Great East Japan
Earthquake(a) The branch for disperison and censoring threshold

Fault model

Numeric calculation method

0.40

Method I
κ include influence ofparameter variation.

Uniform model

0.60

Method IIκ don’t include influenceof parameter variation.

Asperity model

Truncated range

Logarithmic standard
deviation of error
0.10

 = 0.223( = 1.25)

0.30

 = 0.300( = 1.35)

0.75

0.45

 = 0.372( = 1.45)

0.25

0.15

 = 0.438( = 1.55)

0.40

 = 0.223( = 1.25)

0.35

 = 0.300( = 1.35)

0.75

0.20

 = 0.372( = 1.45)

0.25

0.05

 = 0.438( = 1.55)

0.30

 = 0.223( = 1.25)

0.40

 = 0.300( = 1.35)

0.75

0.25

 = 0.372( = 1.45)

0.25

0.05

 = 0.438( = 1.55)

2.3
10

2.3
10

2.3
10

(b) The logic tree based on the Japan Society of Civil Engineers (2011)
Fault model

Numeric calculation method

0.40

Method I
κ include influence ofparameter variation.

Logarithm standard deviation
with error

Censoring range

0.50

 = 0.262( = 1.3)

3

0.50

 = 0.336( = 1.4)

3

0.50

 = 0.262( = 1.3)

3

0.50

 = 0.336( = 1.4)

3

0.50

 = 0.262( = 1.3)

3

0.50

 = 0.336( = 1.4)

3

Uniform model
0.60

Asperity model

Method IIκ don’t include influenceof parameter variation.

(c) The logic tree based on the study after the 2011 Tohoku earthquake
Figure 7.1-15 The logic tree for disperison and censoring threshold

Appendix 7 - 11

7.2. Examples of analyses
Examples of analyses using the G-R model are shown.
(1) Calculation of earthquake probability
The G-R model is taken into consideration only in long-term assessments. When a Poissonprocess is assumed, the annual probability of an earthquake occurring in a case where the mean
recurrence interval is 450 years is 1 - exp (-1/450) = 0.002220.
With the G-R model, the earthquake probability differs according to each magnitude. Table
7.2-1 shows the MW-specific probability for each branch in the magnitude range as calculatedusing the modified G-R equation.
(2) Calculation of tsunami height distribution1) Implementation of numerical tsunami simulations
Tsunami simulations were carried out to obtain tsunami height at target points. In the GR model, the position of tsunami sources and large slip areas were moved without being
constrained by regional divisions.
Figure 7.2-1 shows examples of the positions of tsunami sources for MW9.0 earthquakes.
Calculation grids are given in Figure 7.2-2. Figure 7.2-3 shows the relationship between
tsunami height and MW obtained through tsunami simulations.
2) Conversion to probability of exceedance
The exceedance probability of water level was calculated using the tsunami heights foreach tsunami sources obtained in section 1). Table 7.2-2 shows examples of calculations of theannual probability of exceeding tsunami height 5m on a branch where MW8.7~9.0, κ=1.25, andtruncation threshold 2.3β. When this calculation is performed in various tsunami height
conditions, one tsunami hazard curve, which is shown in Figure 7.2-4, was obtained.
(3) Development of a tsunami water level hazard curves
When the aforementioned calculation is performed for all branches, a hazard analysis iscompleted for one tsunami source region. In the case of the G-R model, the total number ofbranches is 3(42+21) = 30, so the number of hazard curves is 30. The results of calculations
for all branches are given in Figure 7.2-5.
(4) Development of a fractile hazard curves
The weight of each hazard curve is given as the product of the weights of each branch.
Statistical processing gives the fractile hazard curves and the arithmetic mean hazard curve as
Appendix 7 - 12

shown in Figure 7.2-6.
Table 7.2-1 Conditional probability of MW in each branch of MW range (b value=0.9)

MWMW8.7~9.0

MW8.7~9.2

MW8.7~9.3

8.7

0.33220.26300.24458.8

0.27000.21380.19878.9

0.21950.17380.16159.0

0.17840.14130.13139.1-

0.11480.10679.2-

0.09330.08679.3--

0.0705Figure 7.2-1 The examples of tsunami sources (extract from all MW9.0 tsunami sources)

Appendix 7 - 13

Figure 7.2-2 Grid size distribution in the computational region

Figure 7.2-3 Example of correlation of MW and tsunami height

Appendix 7 - 14

Table 7.2-2 Examples for annual probability of exceeding tsunami height 5m (The branches of

MW8.7~9.0, κ=1.25, truncation threshold=2.3β)
CalculatedMW

tsunami height (m)
1

8.7

8.8

8.9

9.0

2
3
4
5
6
7
8
9
10
11
12
13
1
2
3
4
5
6
7
8
9
10
11
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7

1.703
2.356
2.504
2.555
3.781
2.595
3.220
4.918
4.971
3.838
3.184
2.886
2.793
1.709
2.613
2.492
2.799
4.270
3.807
6.492
6.097
3.541
3.640
2.694
2.085
2.205
2.701
3.866
6.870
9.757
4.159
3.736
1.697
2.839
2.763
3.564
9.329
10.9843.487
2.708

Probability ofexceeding 5m
0.00000.00000.00000.00000.09650.00000.01390.4696
0.4894
0.10960.01110.00000.00000.00000.00000.00000.00000.23400.10240.88740.81980.05140.06810.00000.00000.00000.00000.11620.93211.00000.19810.08690.00000.00000.00000.05511.00001.00000.04340.0000
Summation

Probability ofexceeding 5mby an earthquake

Annual probability ofexceeding 5m

 1/13  0.3322

 1/11  0.2700
 0.002220

 1/9  0.2195

 1/7  0.1784

0.1939Appendix 7 - 15

0.1939×0.002220 = 0.000430

Annual Exceedance Probability

10

0

10

-1

10

-2

10

-3

10

-4

10

-5

10

-6

10

-7

Yamada

0

10

20
30
Tsunami Height (m)40Annual Exceedance Probability

Figure 7.2-4 The hazard curve for MW8.7~9.0, κ=1.25, truncation threshold=2.3β

10

0

10

-1

10

-2

10

-3

10

-4

10

-5

10

-6

10

-7

30 branches

Yamada

0

10

20
30
Tsunami Height (m)40Annual Exceedance Probability

Figure 7.2-5 Group of the hazard curves

10

0

10

-1

10

-2

10

-3

10

-4

10

-5

10

-6

10

-7

Yamada
Mean
0.95
0.84
0.50
0.16
0.05

0

10

20
30
Tsunami Height (m)40Figure 7.2-6 The fractile hazard curves and arithmetic mean hazard curve
Appendix 7 - 16

7.3. Analysis results
Instantaneous assessment (January 1, 2016) and a long-term average assessment were performed
for all tsunami sources. Table 7.3-1 shows the method for calculating the earthquake probability foreach tsunami source region. The results of the assessment for all tsunami sources were computed by
the Monte Carlo method.
Figure 7.3-1 shows each result from the instantaneous assessment and the long-term averageassessment, and the comparisons between two arithmetic means in both assessments. In comparing
the arithmetic means, the arithmetic mean for the long-term average assessment was converted into an
exceedance probability in fifty years. From the comparison, no significant difference was seen at Fudai
Village, but the exceedance probability in the long-term average assessment was higher at Yamada
Town. In Figure 7.3-2, arithmetic mean hazard curves are shown for each tsunami source in the longterm average assessment. These figures show that the tsunami earthquakes (JTT) are dominant at Fudai
Village, and the multi-segment earthquakes are dominant at Yamada Town. The probability of tsunami
earthquakes (JTT) was calculated using the Poisson process, so there was no difference in the longterm average assessment and instantaneous hazard analyses. On the other hand, the probability ofmulti-segment earthquakes was computed using a renewal process model, and, the 2011 Tohoku
earthquake occurred, so the probability decreased in instantaneous assessment for the next 50 years.
Consequently, differences such as those shown in Figure 7.3-1(c) have appeared.
Table 7.3-1 The calculation methods of earthquake occurrence probability
Tsunami source region

Calculation method of occurrence probability(a)Poisson process(b)

Poisson process
Renewal process (BPT distribution)(c)

The newest occurrence date: 2011/3/11(d)Poisson process(a) + (b)Poisson process(b) + (c)Poisson process(a) + (b) + (c)Poisson process

Tsunami earthquakes (JTT)

Poisson process

The normal fault earthquakes within
oceanic plate (JTNR)

Poisson process

Appendix 7 - 17

0

10

-1

10

-2

10

-3

10

-4

10

-5

Fudai, Instantaneous
Mean
0.95
0.84
0.50
0.16
0.05

0

20

40
60
Tsunami Height (m)80

Exceedance Probability in 50 Years

Exceedance Probability in 50 Years

10

10

0

10

-1

10

-2

10

-3

10

-4

10

-5

Yamada Instantaneous
Mean
0.95
0.84
0.50
0.16
0.05

0

10

20
30
Tsunami Height (m)40(a) The arithmetic mean and fractile hazard curves by instantaneous assessment

10

0

10

-1

10

-2

10

-3

10

-4

10

-5

10

-6

10

-7

Fudai, Long-term average
Annual Exceedance Probability

Annual Exceedance Probability(Vertical axis: exceedance probability in fifty years)

Mean
0.95
0.84
0.50
0.16
0.05

0

20

40
60
Tsunami Height (m)

80

10

0

10

-1

10

-2

10

-3

10

-4

10

-5

10

-6

10

-7

Yamada, Long-term average
Mean
0.95
0.84
0.50
0.16
0.05

0

10

20
30
Tsunami Height (m)40(b) The arithmetic mean and fractile hazard curves by long-term assessment

10

0

10

-1

10

-2

10

-3

10

-4

10

-5

Fudai
Instantaneous
Long-term average

0

20

40
60
Tsunami Height (m)80

Exceedance Probability in 50 Years

Exceedance Probability in 50 Years(Vertical axis: annual exceedance probability)
10

0

10

-1

10

-2

10

-3

10

-4

10

-5

YamadaInstantaneous
Long-term average

0

10

20
30
Tsunami Height (m)(a) The comparisons between instantaneous and long term average assessments(Vertical axis: exceedance probability in 50 years)
Figure 7.3-1 The probabilistic hazard curves from Kuril Trench to Japan Trench

Appendix 7 - 18

40

0

10

-1

10

-2

10

-3

10

-4

10

-5

10

-6

10

-7

Fudai
Annual Exceedance Probability

Annual Exceedance Probability

10

Total
Multi-segment
rupture type
JTT
JTNR

0

20

40
60
Tsunami Height (m)

80

10

0

10

-1

10

-2

10

-3

10

-4

10

-5

10

-6

10

-7

YamadaTotal
Multi-segment
rupture type
JTT
JTNR

0

10

20
30
Tsunami Height (m)40Figure 7.3-2 The arithmetic mean hazard curves according to tsunami sources by long-term averageassessment[Appendix 7 References]
Cabinet Office Nankai Trough Massive Earthquake Model Review Committee (2012a): Nankai
Trough Massive Earthquake Model Review Committee (Second Report) Tsunami Fault Model
Compilation: Tsunami Fault Models and Tsunami Height and Flooding Areas, etc. (inJapanese).
http://www.bousai.go.jp/jishin/nankai/model/pdf/20120829_2nd_report01.pdf (Accessed on
August 2016).
Cabinet Office Nankai Trough Massive Earthquake Model Review Committee (2012b): Nankai
Trough Massive Earthquake Model Review Committee (12th), Reference 1, Tsunami Fault
Model for 2011 Tohoku earthquake (in Japanese).
http://www.bousai.go.jp/jishin/nankai/model/12/pdf/sub_1.pdf(Accessed on August 2016).
Headquarters for Earthquake Research Promotion Earthquake Research Committee (2004): LongTerm Assessment of Earthquake Activity along Kuril Trench (in Japanese).
http://jishin.go.jp/main/chousa/04dec_chishima2/ (Accessed on August 2016).
Headquarters for Earthquake Research Promotion Earthquake Research Committee (2011): LongTerm Assessment of Earthquake Activity from Area Offshore of Sanriku to Area Offshore of
Boso (Second Edition) (in Japanese).
http://www.jishin.go.jp/main/chousa/11nov_sanriku/(Accessed on August 2016).
Japan Society of Civil Engineers Nuclear Civil Engineering Committee (2011): Methods ofAppendix 7 - 19

Probabilistic Tsunami Hazard Analysis (in Japanese).
http://committees.jsce.or.jp/ceofnp/node/39 (Accessed on August 2016).
Mansinha, L. and D. E. Smylie (1971): The displacement fields of inclined faults, Bulletin of the
Seismological Society of America, Vol. 61, No. 5, pp. 1433-1440.
Usami, T. (1996): Conspectus Japan Destructive Earthquakes, Tokyo University Publishing, 434p. (inJapanese).

Appendix 7 - 20